diff --git a/packages/flutter/lib/src/material/app_bar.dart b/packages/flutter/lib/src/material/app_bar.dart
index 529df96..c004d9d 100644
--- a/packages/flutter/lib/src/material/app_bar.dart
+++ b/packages/flutter/lib/src/material/app_bar.dart
@@ -862,6 +862,7 @@
 
     final bool hasDrawer = scaffold?.hasDrawer ?? false;
     final bool hasEndDrawer = scaffold?.hasEndDrawer ?? false;
+    final bool canPop = parentRoute?.canPop ?? false;
     final bool useCloseButton = parentRoute is PageRoute<dynamic> && parentRoute.fullscreenDialog;
 
     final double toolbarHeight = widget.toolbarHeight ?? appBarTheme.toolbarHeight ?? kToolbarHeight;
@@ -947,8 +948,9 @@
           onPressed: _handleDrawerButton,
           tooltip: MaterialLocalizations.of(context).openAppDrawerTooltip,
         );
-      } else if (parentRoute?.impliesAppBarDismissal ?? false) {
-        leading = useCloseButton ? const CloseButton() : const BackButton();
+      } else {
+        if (!hasEndDrawer && canPop)
+          leading = useCloseButton ? const CloseButton() : const BackButton();
       }
     }
     if (leading != null) {
diff --git a/packages/flutter/lib/src/material/drawer.dart b/packages/flutter/lib/src/material/drawer.dart
index 3297793..6542de8 100644
--- a/packages/flutter/lib/src/material/drawer.dart
+++ b/packages/flutter/lib/src/material/drawer.dart
@@ -401,7 +401,7 @@
     if (_historyEntry == null) {
       final ModalRoute<dynamic>? route = ModalRoute.of(context);
       if (route != null) {
-        _historyEntry = LocalHistoryEntry(onRemove: _handleHistoryEntryRemoved, impliesAppBarDismissal: false);
+        _historyEntry = LocalHistoryEntry(onRemove: _handleHistoryEntryRemoved);
         route.addLocalHistoryEntry(_historyEntry!);
         FocusScope.of(context).setFirstFocus(_focusScopeNode);
       }
diff --git a/packages/flutter/lib/src/widgets/routes.dart b/packages/flutter/lib/src/widgets/routes.dart
index 5104079..53cf942 100644
--- a/packages/flutter/lib/src/widgets/routes.dart
+++ b/packages/flutter/lib/src/widgets/routes.dart
@@ -455,21 +455,13 @@
 /// An entry in the history of a [LocalHistoryRoute].
 class LocalHistoryEntry {
   /// Creates an entry in the history of a [LocalHistoryRoute].
-  ///
-  /// The [impliesAppBarDismissal] defaults to true if not provided.
-  LocalHistoryEntry({ this.onRemove, this.impliesAppBarDismissal = true });
+  LocalHistoryEntry({ this.onRemove });
 
   /// Called when this entry is removed from the history of its associated [LocalHistoryRoute].
   final VoidCallback? onRemove;
 
   LocalHistoryRoute<dynamic>? _owner;
 
-  /// Whether an [AppBar] in the route this entry belongs to should
-  /// automatically add a back button or close button.
-  ///
-  /// Defaults to true.
-  final bool impliesAppBarDismissal;
-
   /// Remove this entry from the history of its associated [LocalHistoryRoute].
   void remove() {
     _owner?.removeLocalHistoryEntry(this);
@@ -490,7 +482,7 @@
 /// is removed from the list and its [LocalHistoryEntry.onRemove] is called.
 mixin LocalHistoryRoute<T> on Route<T> {
   List<LocalHistoryEntry>? _localHistory;
-  int _entriesImpliesAppBarDismissal = 0;
+
   /// Adds a local history entry to this route.
   ///
   /// When asked to pop, if this route has any local history entries, this route
@@ -628,12 +620,7 @@
     _localHistory ??= <LocalHistoryEntry>[];
     final bool wasEmpty = _localHistory!.isEmpty;
     _localHistory!.add(entry);
-    bool internalStateChanged = false;
-    if (entry.impliesAppBarDismissal) {
-      internalStateChanged = _entriesImpliesAppBarDismissal == 0;
-      _entriesImpliesAppBarDismissal += 1;
-    }
-    if (wasEmpty || internalStateChanged)
+    if (wasEmpty)
       changedInternalState();
   }
 
@@ -645,15 +632,10 @@
     assert(entry != null);
     assert(entry._owner == this);
     assert(_localHistory!.contains(entry));
-    bool internalStateChanged = false;
-    if (_localHistory!.remove(entry) && entry.impliesAppBarDismissal) {
-      _entriesImpliesAppBarDismissal -= 1;
-      internalStateChanged = _entriesImpliesAppBarDismissal == 0;
-    }
+    _localHistory!.remove(entry);
     entry._owner = null;
     entry._notifyRemoved();
-    if (_localHistory!.isEmpty || internalStateChanged) {
-      assert(_entriesImpliesAppBarDismissal == 0);
+    if (_localHistory!.isEmpty) {
       if (SchedulerBinding.instance.schedulerPhase == SchedulerPhase.persistentCallbacks) {
         // The local history might be removed as a result of disposing inactive
         // elements during finalizeTree. The state is locked at this moment, and
@@ -681,12 +663,7 @@
       assert(entry._owner == this);
       entry._owner = null;
       entry._notifyRemoved();
-      bool internalStateChanged = false;
-      if (entry.impliesAppBarDismissal) {
-        _entriesImpliesAppBarDismissal -= 1;
-        internalStateChanged = _entriesImpliesAppBarDismissal == 0;
-      }
-      if (_localHistory!.isEmpty || internalStateChanged)
+      if (_localHistory!.isEmpty)
         changedInternalState();
       return false;
     }
@@ -720,7 +697,6 @@
   const _ModalScopeStatus({
     required this.isCurrent,
     required this.canPop,
-    required this.impliesAppBarDismissal,
     required this.route,
     required super.child,
   }) : assert(isCurrent != null),
@@ -730,14 +706,12 @@
 
   final bool isCurrent;
   final bool canPop;
-  final bool impliesAppBarDismissal;
   final Route<dynamic> route;
 
   @override
   bool updateShouldNotify(_ModalScopeStatus old) {
     return isCurrent != old.isCurrent ||
            canPop != old.canPop ||
-           impliesAppBarDismissal != old.impliesAppBarDismissal ||
            route != old.route;
   }
 
@@ -746,7 +720,6 @@
     super.debugFillProperties(description);
     description.add(FlagProperty('isCurrent', value: isCurrent, ifTrue: 'active', ifFalse: 'inactive'));
     description.add(FlagProperty('canPop', value: canPop, ifTrue: 'can pop'));
-    description.add(FlagProperty('impliesAppBarDismissal', value: impliesAppBarDismissal, ifTrue: 'implies app bar dismissal'));
   }
 }
 
@@ -849,7 +822,6 @@
         route: widget.route,
         isCurrent: widget.route.isCurrent, // _routeSetState is called if this updates
         canPop: widget.route.canPop, // _routeSetState is called if this updates
-        impliesAppBarDismissal: widget.route.impliesAppBarDismissal,
         child: Offstage(
           offstage: widget.route.offstage, // _routeSetState is called if this updates
           child: PageStorage(
@@ -1589,14 +1561,6 @@
   /// notified.
   bool get canPop => hasActiveRouteBelow || willHandlePopInternally;
 
-  /// Whether an [AppBar] in the route should automatically add a back button or
-  /// close button.
-  ///
-  /// This getter returns true if there is at least one active route below it,
-  /// or there is at least one [LocalHistoryEntry] with `impliesAppBarDismissal`
-  /// set to true
-  bool get impliesAppBarDismissal => hasActiveRouteBelow || _entriesImpliesAppBarDismissal > 0;
-
   // Internals
 
   final GlobalKey<_ModalScopeState<T>> _scopeKey = GlobalKey<_ModalScopeState<T>>();
diff --git a/packages/flutter/test/material/app_bar_test.dart b/packages/flutter/test/material/app_bar_test.dart
index 53a653b..635e17c 100644
--- a/packages/flutter/test/material/app_bar_test.dart
+++ b/packages/flutter/test/material/app_bar_test.dart
@@ -3074,44 +3074,6 @@
     });
   });
 
-  // Regression test for https://github.com/flutter/flutter/issues/80256
-  testWidgets('The second page should have a back button even it has a end drawer', (WidgetTester tester) async {
-    final Page<void> page1 = MaterialPage<void>(
-        key: const ValueKey<String>('1'),
-        child: Scaffold(
-          key: const ValueKey<String>('1'),
-          appBar: AppBar(),
-          endDrawer: const Drawer(),
-        )
-    );
-    final Page<void> page2 = MaterialPage<void>(
-        key: const ValueKey<String>('2'),
-        child: Scaffold(
-          key: const ValueKey<String>('2'),
-          appBar: AppBar(),
-          endDrawer: const Drawer(),
-        )
-    );
-    final List<Page<void>> pages = <Page<void>>[ page1, page2 ];
-    await tester.pumpWidget(
-      MaterialApp(
-        home: Navigator(
-          pages: pages,
-          onPopPage: (Route<Object?> route, Object? result) => false,
-        ),
-      ),
-    );
-
-    // The page2 should have a back button.
-    expect(
-        find.descendant(
-          of: find.byKey(const ValueKey<String>('2')),
-          matching: find.byType(BackButton),
-        ),
-        findsOneWidget
-    );
-  });
-
   testWidgets('AppBar.preferredHeightFor', (WidgetTester tester) async {
     late double preferredHeight;
     late Size preferredSize;