Use both OnKeyDown and GlobalAction.Back

osu.Game/Screens/Loader.cs

@@ -19,6 +19,8 @@ namespace osu.Game.Screens
 
         public override bool ShowOverlaysOnEnter => false;
 
+        protected override bool AllowBackButton => false;
+
         public Loader()
         {
             ValidForResume = false;

osu.Game/Screens/Menu/MainMenu.cs

@@ -26,6 +26,8 @@ namespace osu.Game.Screens.Menu
 
         public override bool ShowOverlaysOnEnter => buttons.State != MenuState.Initial;
 
+        protected override bool AllowBackButton => buttons.State != MenuState.Initial;
+
         private readonly BackgroundScreenDefault background;
         private Screen songSelect;
 

osu.Game/Screens/OsuScreen.cs

@@ -7,6 +7,7 @@ using osu.Framework.Audio;
 using osu.Framework.Audio.Sample;
 using osu.Framework.Configuration;
 using osu.Framework.Graphics;
+using osu.Framework.Input;
 using osu.Framework.Input.Bindings;
 using osu.Framework.Screens;
 using osu.Game.Beatmaps;
@@ -15,6 +16,7 @@ using osu.Game.Input.Bindings;
 using osu.Game.Rulesets;
 using osu.Game.Screens.Menu;
 using OpenTK;
+using OpenTK.Input;
 
 namespace osu.Game.Screens
 {
@@ -105,6 +107,20 @@ namespace osu.Game.Screens
 
         public bool OnReleased(GlobalAction action) => action == GlobalAction.Back && AllowBackButton;
 
+        protected override bool OnKeyDown(InputState state, KeyDownEventArgs args)
+        {
+            if (args.Repeat || !IsCurrentScreen) return false;
+
+            switch (args.Key)
+            {
+                case Key.Escape:
+                    Exit();
+                    return true;
+            }
+
+            return base.OnKeyDown(state, args);
+        }
+
         protected override void OnResuming(Screen last)
         {
             sampleExit?.Play();

osu.Game/Screens/Play/ScreenWithBeatmapBackground.cs

@@ -16,6 +16,7 @@ namespace osu.Game.Screens.Play
         protected override BackgroundScreen CreateBackground() => new BackgroundScreenBeatmap(Beatmap);
 
         public override bool AllowBeatmapRulesetChange => false;
+        protected override bool AllowBackButton => false;
 
         protected const float BACKGROUND_FADE_DURATION = 800;