Sadly for people who are like the man you mention, "a few more weeks" is in actual fact a lot longer. The problem is more likely to be the lack of a proper support network to help this individual care for themselves in the long-term, as well as helping maintain routines and structure in their life. This is not something that can be done in an environment as tightly constructed as a mental institution. It requires a combination of professionals and friends on the outside, who are able to give this person round the clock support to help deal the the complexity of life in a uncontrollable environment.
Unless we (as a society) can find a way to provide this for those who have been pushed to the fringes of reality, there will still be a significant portion of people pushed into the Treat-Release-Repeat loop for years to come.
I had a swimming instructor who told me her brother was mentally ill and was in and out of these all the time. He'd feel he'd need to stay there a few more weeks, but they'd push him right out. He'd do okay for a while, then stop taking his meds (because most of those meds do make you feel like shit), then he'd start having delusions again.
Eventually he'd be back to begging for 40ozs and eventually be back in the center. America's system doesn't provide enough funding, not just for mental health, but all the other services around health to help people out and be self sustainable in their communities.