The point is that the hospital doesn’t keep you until you are at 100% health; they discharge you as soon as is pragmatic. You don’t spend weeks in the hospital after routine appendectomy until your incisions are completely healed and you are back to full strength. The longer you stay in the hospital the greater your chances are of coming down with some hospital-associated infection, and the daily costs don’t decrease while the incremental daily recovery does. Hospital beds are not an infinite resource, either, and they keep making new sick people who need those beds too. There’s a point at which it’s best to send you home (or to rehab, or a nursing home) to complete your recovery under less intensively monitored/expensive conditions, and the earlier that is the better.
There’s some German results somewhere that say they haven’t been able to grow COVID-19 viruses from people more than 3 days after they get well. This is (I hope) the basis for the CDC advice that you can stop quarantine after there is no result on the CDC test, taken after the patient has had no symptoms for a couple of days.
The CDC test itself is only designed to detect infection, not to show that people are safe, and related tests show that you’ve still got a lot of the genetic material from the virus in you for a couple of weeks.
This article discusses those German results:
I think it’s far too early to tell
I had the flu in April 2000 and it knocked me for a loop. I was out of work for seven days, plus weekends and when I recovered, I honestly didn’t feel back to normal till about August.
So even the “ordinary” flu takes awhile to come back from.