Uses the services available to him (free housing, food, job programs, transportation etc) to get a real job, leave his life of crime behind him, and eventually pay back his debt to society through the same taxes he utilized.

Seems to me he's in the same spot he is now, except materially less employable due to a prison sentence. Do you think your idea here really seems probable to work?

It gets him off the street (as well as others like him) and stops the hemorrhaging of businesses from those cities. This is the exact thing that leads to food deserts that will impact poor people actually doing the right thing with their lives and leads them to commit crimes of their own because why should they obey the social contract when guys like this are obviously not and making much more from it?

If he will be the same when he gets out, and you know this, why let him out?

Suppose your roof leaks and you can't afford to fix it. Or maybe you pay some professionals to come fix it, they faff around for a bit, say they 'rehabilitated' your roof, but a while later it starts leaking again.

So you get a bucket and put it under the dripping hole. The bucket doesn't fix the roof. The bucket will eventually fill up and you'll have to empty it down a drain before trying it again. Again and again. The bucket isn't solving anything, but would you be better off without the bucket? No, the bucket at least keeps your floor dry some of the time. That's better than nothing. Prison is a bucket. Prisons collect criminals for a while until they eventually fill up. But they're better than dumping all those criminals straight into the streets.

Because we don't have a long term mental health committal system like we should and the criminal system cant hold him forever on small charges.

Can you imagine any circumstance whatsoever, under which you might develop a habit of stealing things?

Would you like to be committed to a mental institution forever, in that circumstance?

What most of us ignore is that people have to want to help themselves. Otherwise, their lives will never permanently improve. And unfortunately, this desire doesn't usually happen until people hit bottom. Simple human nature.

If he doesn't want to help himself I see only 2 options then, either A) cut him off of all services and let him hit bottom to the point where he will want help or B) go to prison, get out and get better himself (if not, repeat)