some games don't work correctly with the Twitch Studio in game overlay and trying to stream them with one monitor can be a pain.
You could solve this problem by having the overlay always appear on screen no matter what.
It doesn't seem as if the overlay has anything to do with the games themselves so it would be really handy to have it always there no matter what.
This would also solve the problem of the overlay not working while not directly streaming a video game.
If this is already a feature then I apologize, but the in game overlay is kind of important when streaming with one monitor so when it does not work at all it can be very frustrating