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.
I know of only one normal person on the streets. The rest take dumps on escalators, do drugs, act up and show the results of mostly drug abuse.