You can ask Safari to do that by enabling 'Reading List: Save articles for offline reading automatically'. It's not WARC but it is an offline archive. The shortcut is cmd-shift-D which is almost the same as the bookmark one. It's also the only way I know of to get Safari to show you bookmarks in reverse chronological order. And it syncs to iOS devices.

This could be done in better and more specialized ways, one problem is browser extension APIs don't provide very good access to the browser's webpage-saving features.