Opening an image on the browser its a very good option for a custom background image, but it would be very nice that, every time you toggle form ‘share screen’ to cam, it would go to the last screen shared, as default.
Regarding having the same image shared every time, you would then need a way to change that behavior. It’s a niche case (your workaround) so I doubt there would be much traction to add that feature but you can still file a feature request.
A “lobby”'feature is coming up, maybe it would make sense there. Perhaps mention this if you file a feature request.