diff --git a/packages/compose/src/hooks/use-keyboard-shortcut/index.js b/packages/compose/src/hooks/use-keyboard-shortcut/index.js
index 95dd997eac11c9..294823c144009f 100644
--- a/packages/compose/src/hooks/use-keyboard-shortcut/index.js
+++ b/packages/compose/src/hooks/use-keyboard-shortcut/index.js
@@ -8,12 +8,7 @@ import { includes, castArray } from 'lodash';
 /**
  * WordPress dependencies
  */
-import {
-	useEffect,
-	useRef,
-	createContext,
-	useContext,
-} from '@wordpress/element';
+import { useEffect, useRef } from '@wordpress/element';
 
 /**
  * A block selection object.
@@ -26,8 +21,6 @@ import {
  * @property {Object}  [target]      React reference to the DOM element used to catch the keyboard event.
  */
 
-const WindowContext = createContext();
-
 /**
  * Return true if platform is MacOS.
  *
@@ -59,27 +52,18 @@ function useKeyboardShortcut(
 		eventName = 'keydown',
 		isDisabled = false, // This is important for performance considerations.
 		target,
-		altWindow,
 	} = {}
 ) {
 	const currentCallback = useRef( callback );
 	useEffect( () => {
 		currentCallback.current = callback;
 	}, [ callback ] );
-	const win = useContext( WindowContext );
 
 	useEffect( () => {
 		if ( isDisabled ) {
 			return;
 		}
-
-		let node = ( altWindow || win || window ).document;
-
-		if ( target && target.current ) {
-			node = target.current;
-		}
-
-		const mousetrap = new Mousetrap( node );
+		const mousetrap = new Mousetrap( target ? target.current : document );
 		castArray( shortcuts ).forEach( ( shortcut ) => {
 			const keys = shortcut.split( '+' );
 			// Determines whether a key is a modifier by the length of the string.
@@ -116,6 +100,4 @@ function useKeyboardShortcut(
 	}, [ shortcuts, bindGlobal, eventName, target, isDisabled ] );
 }
 
-useKeyboardShortcut.WindowContext = WindowContext;
-
 export default useKeyboardShortcut;
diff --git a/packages/edit-site/src/components/block-editor/index.js b/packages/edit-site/src/components/block-editor/index.js
index 07847a82b3bcf5..2876611128b319 100644
--- a/packages/edit-site/src/components/block-editor/index.js
+++ b/packages/edit-site/src/components/block-editor/index.js
@@ -20,7 +20,6 @@ import {
 	BlockSelectionClearer,
 	__experimentalUseResizeCanvas as useResizeCanvas,
 } from '@wordpress/block-editor';
-import { useKeyboardShortcut } from '@wordpress/compose';
 import { __ } from '@wordpress/i18n';
 
 /**
@@ -37,13 +36,12 @@ export const IFrame = ( {
 	...props
 } ) => {
 	const [ contentRef, setContentRef ] = useState();
-	const win = contentRef && contentRef.contentWindow;
 	const doc = contentRef && contentRef.contentWindow.document;
 
 	useEffect( () => {
 		if ( doc ) {
 			doc.body.className = bodyClassName;
-			doc.body.style.margin = '0px';
+			doc.body.style.margin = '0';
 			doc.head.innerHTML = head;
 			doc.dir = document.dir;
 
@@ -53,14 +51,14 @@ export const IFrame = ( {
 				doc.head.appendChild( styleEl );
 			} );
 
-			[ ...document.styleSheets ].reduce( ( acc, styleSheet ) => {
+			// Search the document for stylesheets targetting the editor canvas.
+			Array.from( document.styleSheets ).reduce( ( acc, styleSheet ) => {
+				// May fail for external styles.
 				try {
 					const isMatch = [ ...styleSheet.cssRules ].find(
 						( { selectorText } ) => {
-							return (
-								selectorText.indexOf(
-									'.editor-styles-wrapper'
-								) !== -1
+							return selectorText.includes(
+								'.editor-styles-wrapper'
 							);
 						}
 					);
@@ -87,9 +85,7 @@ export const IFrame = ( {
 			name="editor-canvas"
 			data-loaded={ !! contentRef }
 		>
-			<useKeyboardShortcut.WindowContext.Provider value={ win }>
-				{ doc && createPortal( children, doc.body ) }
-			</useKeyboardShortcut.WindowContext.Provider>
+			{ doc && createPortal( children, doc.body ) }
 		</iframe>
 	);
 };