diff --git a/cpp/src/arrow/util/bit_util_benchmark.cc b/cpp/src/arrow/util/bit_util_benchmark.cc
index da624bec1986..bc4cdad99c5f 100644
--- a/cpp/src/arrow/util/bit_util_benchmark.cc
+++ b/cpp/src/arrow/util/bit_util_benchmark.cc
@@ -172,7 +172,7 @@ static void BenchmarkBitmapVisitBitsetAnd(benchmark::State& state) {
 static void BenchmarkBitmapVisitUInt8And(benchmark::State& state) {
   BenchmarkAndImpl(state, [](const internal::Bitmap(&bitmaps)[2], internal::Bitmap* out) {
     int64_t i = 0;
-    internal::Bitmap::VisitWords(bitmaps, [&](std::array<uint8_t, 2> uint8s) {
+    internal::Bitmap::VisitWords<uint8_t>(bitmaps, [&](std::array<uint8_t, 2> uint8s) {
       reinterpret_cast<uint8_t*>(out->mutable_data())[i++] = uint8s[0] & uint8s[1];
     });
   });
diff --git a/cpp/src/arrow/util/bitmap.h b/cpp/src/arrow/util/bitmap.h
index 49f319081fa4..4cba55a8adc5 100644
--- a/cpp/src/arrow/util/bitmap.h
+++ b/cpp/src/arrow/util/bitmap.h
@@ -21,12 +21,14 @@
 #include <array>
 #include <bitset>
 #include <cassert>
+#include <concepts>
 #include <cstdint>
 #include <cstring>
 #include <memory>
 #include <span>
 #include <string>
 #include <string_view>
+#include <type_traits>
 #include <utility>
 
 #include "arrow/buffer.h"
@@ -36,7 +38,6 @@
 #include "arrow/util/bitmap_writer.h"
 #include "arrow/util/compare.h"
 #include "arrow/util/endian.h"
-#include "arrow/util/functional.h"
 #include "arrow/util/string_util.h"
 #include "arrow/util/visibility.h"
 
@@ -145,9 +146,8 @@ class ARROW_EXPORT Bitmap : public util::ToStringOstreamable<Bitmap>,
   // carefully in other cases.
   // For 2 bitmaps or less, and/or smaller bitmaps, see also VisitTwoBitBlocksVoid
   // and BitmapUInt64Reader.
-  template <size_t N, typename Visitor,
-            typename Word = typename std::decay<
-                internal::call_traits::argument_type<0, Visitor&&>>::type::value_type>
+  template <typename Word = uint64_t, size_t N, typename Visitor>
+    requires std::same_as<void, std::invoke_result_t<Visitor, std::array<Word, N>&>>
   static int64_t VisitWords(const Bitmap (&bitmaps_arg)[N], Visitor&& visitor) {
     constexpr int64_t kBitWidth = sizeof(Word) * 8;
 
@@ -248,13 +248,12 @@ class ARROW_EXPORT Bitmap : public util::ToStringOstreamable<Bitmap>,
     return min_offset;
   }
 
-  template <size_t N, size_t M, typename ReaderT, typename WriterT, typename Visitor,
-            typename Word = typename std::decay<
-                internal::call_traits::argument_type<0, Visitor&&>>::type::value_type>
+  template <size_t N, size_t M, typename ReaderT, typename WriterT, typename Visitor>
   static void RunVisitWordsAndWriteLoop(int64_t bit_length,
                                         std::array<ReaderT, N>& readers,
                                         std::array<WriterT, M>& writers,
                                         Visitor&& visitor) {
+    using Word = decltype(readers[0].NextWord());
     constexpr int64_t kBitWidth = sizeof(Word) * 8;
 
     std::array<Word, N> visited_words;
@@ -318,6 +317,7 @@ class ARROW_EXPORT Bitmap : public util::ToStringOstreamable<Bitmap>,
   /// may be offset within the first visited word, but words will otherwise contain
   /// densely packed bits loaded from the bitmap. That offset within the first word is
   /// returned.
+  ///
   /// Visitor is expected to have the following signature
   ///     [](const std::array<Word, N>& in_words, std::array<Word, M>* out_words){...}
   ///
@@ -326,9 +326,9 @@ class ARROW_EXPORT Bitmap : public util::ToStringOstreamable<Bitmap>,
   // carefully in other cases.
   // For 2 bitmaps or less, and/or smaller bitmaps, see also VisitTwoBitBlocksVoid
   // and BitmapUInt64Reader.
-  template <size_t N, size_t M, typename Visitor,
-            typename Word = typename std::decay<
-                internal::call_traits::argument_type<0, Visitor&&>>::type::value_type>
+  template <typename Word = uint64_t, size_t N, size_t M, typename Visitor>
+    requires std::same_as<
+        void, std::invoke_result_t<Visitor, std::array<Word, N>&, std::array<Word, M>*>>
   static void VisitWordsAndWrite(const std::array<Bitmap, N>& bitmaps_arg,
                                  std::array<Bitmap, M>* out_bitmaps_arg,
                                  Visitor&& visitor) {
diff --git a/cpp/src/arrow/util/cache_benchmark.cc b/cpp/src/arrow/util/cache_benchmark.cc
index 7439ee2f5013..071367d8ec60 100644
--- a/cpp/src/arrow/util/cache_benchmark.cc
+++ b/cpp/src/arrow/util/cache_benchmark.cc
@@ -126,7 +126,7 @@ static void BenchmarkMemoize(benchmark::State& state, Memoized&& mem,
 static void MemoizeLruCached(benchmark::State& state) {
   const auto keys = MakeStrings(kCacheSize, state.range(0));
   const auto values = MakeStrings(kCacheSize, state.range(1));
-  auto mem = MemoizeLru(Callable(values), kCacheSize);
+  auto mem = MemoizeLru<std::string>(Callable(values), kCacheSize);
   BenchmarkMemoize(state, mem, keys);
 }
 
@@ -135,7 +135,8 @@ static void MemoizeLruCachedThreadUnsafe(benchmark::State& state) {
   const auto values = MakeStrings(kCacheSize, state.range(1));
   // Emulate recommended usage of MemoizeLruCachedThreadUnsafe
   // (the compiler is probably able to cache the TLS-looked up value, though)
-  thread_local auto mem = MemoizeLruThreadUnsafe(Callable(values), kCacheSize);
+  thread_local auto mem =
+      MemoizeLruThreadUnsafe<std::string>(Callable(values), kCacheSize);
   BenchmarkMemoize(state, mem, keys);
 }
 
diff --git a/cpp/src/arrow/util/cache_internal.h b/cpp/src/arrow/util/cache_internal.h
index fe10af8bb2aa..6c65712060f0 100644
--- a/cpp/src/arrow/util/cache_internal.h
+++ b/cpp/src/arrow/util/cache_internal.h
@@ -26,7 +26,6 @@
 #include <utility>
 #include <vector>
 
-#include "arrow/util/functional.h"
 #include "arrow/util/logging.h"
 #include "arrow/util/macros.h"
 
@@ -167,11 +166,12 @@ struct ThreadUnsafeMemoizer {
 };
 
 template <template <typename...> class Cache, template <typename...> class MemoizerType,
-          typename Func, typename Key = std::decay_t<call_traits::argument_type<0, Func>>,
-          typename Value = std::decay_t<std::invoke_result_t<Func, const Key&>>,
-          typename Memoizer = MemoizerType<Key, Value, Cache<Key, Value>, Func>,
-          typename RetType = typename Memoizer::RetType>
-static std::function<RetType(const Key&)> Memoize(Func&& func, int32_t cache_capacity) {
+          typename Key, typename Func>
+static auto Memoize(Func&& func, int32_t cache_capacity) {
+  using Value = std::decay_t<std::invoke_result_t<Func, const Key&>>;
+  using Memoizer = MemoizerType<Key, Value, Cache<Key, Value>, Func>;
+  using RetType = typename Memoizer::RetType;
+
   // std::function<> requires copy constructibility
   struct {
     RetType operator()(const Key& key) const { return (*memoized_)(key); }
@@ -179,30 +179,29 @@ static std::function<RetType(const Key&)> Memoize(Func&& func, int32_t cache_cap
   } shared_memoized = {
       std::make_shared<Memoizer>(std::forward<Func>(func), cache_capacity)};
 
-  return shared_memoized;
+  return std::function<RetType(const Key&)>(std::move(shared_memoized));
 }
 
 }  // namespace detail
 
 // Apply a LRU memoization cache to a callable.
-template <typename Func>
-static auto MemoizeLru(Func&& func, int32_t cache_capacity)
-    -> decltype(detail::Memoize<LruCache, detail::ThreadSafeMemoizer>(
-        std::forward<Func>(func), cache_capacity)) {
-  return detail::Memoize<LruCache, detail::ThreadSafeMemoizer>(std::forward<Func>(func),
-                                                               cache_capacity);
+// `Key` is the type of the callable's (single) argument.
+template <typename Key, typename Func>
+  requires std::is_invocable_v<Func, const Key&>
+static auto MemoizeLru(Func&& func, int32_t cache_capacity) {
+  return detail::Memoize<LruCache, detail::ThreadSafeMemoizer, Key>(
+      std::forward<Func>(func), cache_capacity);
 }
 
 // Like MemoizeLru, but not thread-safe.  This version allows for much faster
 // lookups (more than 2x faster), but you'll have to manage thread safety yourself.
 // A recommended usage is to declare per-thread caches using `thread_local`
 // (see cache_benchmark.cc).
-template <typename Func>
-static auto MemoizeLruThreadUnsafe(Func&& func, int32_t cache_capacity)
-    -> decltype(detail::Memoize<LruCache, detail::ThreadUnsafeMemoizer>(
-        std::forward<Func>(func), cache_capacity)) {
-  return detail::Memoize<LruCache, detail::ThreadUnsafeMemoizer>(std::forward<Func>(func),
-                                                                 cache_capacity);
+template <typename Key, typename Func>
+  requires std::is_invocable_v<Func, const Key&>
+static auto MemoizeLruThreadUnsafe(Func&& func, int32_t cache_capacity) {
+  return detail::Memoize<LruCache, detail::ThreadUnsafeMemoizer, Key>(
+      std::forward<Func>(func), cache_capacity);
 }
 
 }  // namespace internal
diff --git a/cpp/src/arrow/util/cache_test.cc b/cpp/src/arrow/util/cache_test.cc
index 264bfe68ec5d..d009806ab347 100644
--- a/cpp/src/arrow/util/cache_test.cc
+++ b/cpp/src/arrow/util/cache_test.cc
@@ -183,18 +183,16 @@ struct Callable {
 };
 
 struct MemoizeLruFactory {
-  template <typename Func,
-            typename RetType = decltype(MemoizeLru(std::declval<Func>(), 0))>
-  RetType operator()(Func&& func, int32_t capacity) {
-    return MemoizeLru(std::forward<Func>(func), capacity);
+  template <typename Func>
+  auto operator()(Func&& func, int32_t capacity) {
+    return MemoizeLru<std::string>(std::forward<Func>(func), capacity);
   }
 };
 
 struct MemoizeLruThreadUnsafeFactory {
-  template <typename Func,
-            typename RetType = decltype(MemoizeLruThreadUnsafe(std::declval<Func>(), 0))>
-  RetType operator()(Func&& func, int32_t capacity) {
-    return MemoizeLruThreadUnsafe(std::forward<Func>(func), capacity);
+  template <typename Func>
+  auto operator()(Func&& func, int32_t capacity) {
+    return MemoizeLruThreadUnsafe<std::string>(std::forward<Func>(func), capacity);
   }
 };
 
diff --git a/cpp/src/arrow/util/functional.h b/cpp/src/arrow/util/functional.h
index 4444b747c837..1240f6c6ca8c 100644
--- a/cpp/src/arrow/util/functional.h
+++ b/cpp/src/arrow/util/functional.h
@@ -18,7 +18,6 @@
 #pragma once
 
 #include <memory>
-#include <tuple>
 #include <type_traits>
 
 #include "arrow/result.h"
@@ -36,28 +35,6 @@ struct Empty {
   }
 };
 
-/// Helper struct for examining lambdas and other callables.
-/// TODO(ARROW-12655) support function pointers
-struct call_traits {
- public:
-  template <std::size_t I, typename F, typename R, typename... A>
-  static typename std::tuple_element<I, std::tuple<A...>>::type argument_type_impl(
-      R (F::*)(A...));
-
-  template <std::size_t I, typename F, typename R, typename... A>
-  static typename std::tuple_element<I, std::tuple<A...>>::type argument_type_impl(
-      R (F::*)(A...) const);
-
-  template <std::size_t I, typename F, typename R, typename... A>
-  static typename std::tuple_element<I, std::tuple<A...>>::type argument_type_impl(
-      R (F::*)(A...) &&);
-
-  /// If F is not overloaded, the argument types of its call operator can be
-  /// extracted via call_traits::argument_type<Index, F>
-  template <std::size_t I, typename F>
-  using argument_type = decltype(argument_type_impl<I>(&std::decay<F>::type::operator()));
-};
-
 /// A type erased callable object which may only be invoked once.
 /// It can be constructed from any lambda which matches the provided call signature.
 /// Invoking it results in destruction of the lambda, freeing any state/references
diff --git a/cpp/src/arrow/util/future.h b/cpp/src/arrow/util/future.h
index fa45427a9d3d..1884f5969791 100644
--- a/cpp/src/arrow/util/future.h
+++ b/cpp/src/arrow/util/future.h
@@ -61,10 +61,6 @@ struct SyncType<internal::Empty> {
   using type = Status;
 };
 
-template <typename Fn>
-using first_arg_is_status =
-    std::is_same<std::decay_t<internal::call_traits::argument_type<0, Fn>>, Status>;
-
 template <typename Fn, typename Then, typename Else>
 using if_has_no_args = std::conditional_t<std::is_invocable_v<Fn>, Then, Else>;
 
@@ -446,10 +442,12 @@ class [[nodiscard]] Future {
     };
   };
 
+  // conditional whether OnComplete is invokable with Status _and not with Result_
   template <typename OnComplete>
   using WrapOnComplete = typename std::conditional<
-      detail::first_arg_is_status<OnComplete>::value, WrapStatusyOnComplete,
-      WrapResultOnComplete>::type::template Callback<OnComplete>;
+      std::is_invocable_v<OnComplete, const Status&> &&
+          !std::is_invocable_v<OnComplete, const Result<ValueType>&>,
+      WrapStatusyOnComplete, WrapResultOnComplete>::type::template Callback<OnComplete>;
 
   /// \brief Consumer API: Register a callback to run when this future completes
   ///
@@ -514,15 +512,8 @@ class [[nodiscard]] Future {
                                ContinuedFuture>::value,
                   "OnSuccess and OnFailure must continue with the same future type");
 
-    struct DummyOnSuccess {
-      void operator()(const T&);
-    };
-    using OnSuccessArg = typename std::decay<internal::call_traits::argument_type<
-        0, detail::if_has_no_args<OnSuccess, DummyOnSuccess, OnSuccess>>>::type;
-
-    static_assert(
-        !std::is_same<OnSuccessArg, typename EnsureResult<OnSuccessArg>::type>::value,
-        "OnSuccess' argument should not be a Result");
+    static_assert(!std::is_invocable_v<OnSuccess, const Result<T>&>,
+                  "OnSuccess' argument should not be a Result");
 
     void operator()(const Result<T>& result) && {
       detail::ContinueFuture continue_future;
diff --git a/cpp/src/arrow/util/future_test.cc b/cpp/src/arrow/util/future_test.cc
index 2ed2b69aed52..1b55ddc6d88f 100644
--- a/cpp/src/arrow/util/future_test.cc
+++ b/cpp/src/arrow/util/future_test.cc
@@ -1539,13 +1539,11 @@ TEST(FnOnceTest, MoveOnlyDataType) {
         return *i0.data + *i1.data + (i0.moves * 1000) + (i1.moves * 100);
       };
 
-  using arg0 = call_traits::argument_type<0, decltype(fn)>;
-  using arg1 = call_traits::argument_type<1, decltype(fn)>;
-  using arg2 = call_traits::argument_type<2, decltype(fn)>;
-  static_assert(std::is_same<arg0, const MoveOnlyDataType&>::value, "");
-  static_assert(std::is_same<arg1, MoveOnlyDataType>::value, "");
-  static_assert(std::is_same<arg2, std::string>::value,
-                "should not add a && to the call type (demanding rvalue unnecessarily)");
+  static_assert(std::is_invocable_r_v<int, decltype(fn), const MoveOnlyDataType&,
+                                      MoveOnlyDataType, std::string&>);
+  // a move-only by-value argument must be moved in
+  static_assert(!std::is_invocable_v<decltype(fn), const MoveOnlyDataType&,
+                                     MoveOnlyDataType&, std::string&>);
 
   MoveOnlyDataType i0{1}, i1{41};
   std::string copyable = "";