what if hospitals rented out their empty rooms to guest when they weren't busy?

not a good idea. There are many infections traveling in hospitals. Incoming stays will increase the risk, they clean differently in hospitals rather than in hotels. Incoming bacteria and viruses germinations and also, guests can get infected as well. No, not a good idea.

Do not know of many hospitals with vacancies..

That's strange... empty hospitals? You're in Florida, right? The hospital I know is sometimes short of beds. (Texas) I wondering if whatever is going on where you're at is coming our way...

Getting rid of them becomes a problem