Except, again, that doesn't solve the problem. They go to jail for a year or two, become a handful for people in prison to handle (whom are not equipped to handle people with severe mental illness), are released and then the cycle continues. Or even then, those inmates are admitted to those same hospitals because where else do you think people get proper treatment?
None of this discussion solves the actual problem at hand, it just deals with the symptoms. Eventually the problem will become uncontrollable if you just ignore the actual damn reasons why people with said issues end up becoming homeless or violent in the first place.
When the symptoms include unacceptable impacts on other people, they still have to be dealt with.
We can and should chip away at risk factors, but the human brain is wickedly complex and we're never going to get 100% health and behavior within norms. Just like we can and should encourage exercise and healthy diets, but we're still going to need the medical system.
Instead they person is battering inmates or police and getting punished for it, while potentially being recruited to criminal activity instead of being treated.
None of this discussion solves the actual problem at hand, it just deals with the symptoms. Eventually the problem will become uncontrollable if you just ignore the actual damn reasons why people with said issues end up becoming homeless or violent in the first place.