I’ve talked with some these folks. They get into a home, get violent and thrown out.
They can’t in many cases live like normal people because they have hair triggers and won’t properly self medicate.
I’m not sure the insane who are off their meds qualify as homeless by choice.
The point that there are those who are homeless by choice is nonetheless valid, and some of them are even reasonably decent folks — there is still a remnant of the old hobo culture (homeless and itinerant by choice, willing to work as day laborers or take odd jobs to support themselves, begging only when no work is available). Very few, but still there. A couple years back my younger son helped one such fellow find his cat when he lost it passing through our town.
Actually, the shelters won’t let them drink or do drugs so they sleep outside.
Many homeless need to be in mental health facilities for life.
There’s a reason homelessness skyrocketed after “One Flew Over the Cuckoo’s Nest” led to most mental hospitals getting closed, on the idea that most of these people could be handled via outpatient care - and ignoring the fact that many had to be supervised or forced to take their meds.
Now we have fewer beds than we did in the 1950s but far more people in general.