This is a very interesting take -- I wonder how it would deal with web browsers? I'm curious because I actually did try to add firefox to my Steam Deck as a "game" and it couldn't deal with multiple windows?
Aside from most emulators of note having been released as a libretro “core”, the sole non-game core I’m aware of is some kind of ffmpeg video player. If things like 3d console emulators and ffmpeg can draw to the surface that libretro provides, doesn’t seem like it should be insurmountable to get something like WebKit rendering content there (I briefly looked into doing this with Firefox years ago but found it’s hellish to embed—chrome’s a little better, but it’s chrome and heavy as hell. WebKit seems to me like the most promising engine for such a project, lighter than the other two and relatively embedding-friendly). Get that working, and the main remaining hurdle would be getting an overlay modal menu or something like that working to allow interaction and drive the engine.