You're proposing putting them in prison, and for a reason, because otherwise they just blow it off. It turns out that's really expensive though, e.g. California

You're proposing putting them in prison, and for a reason, because otherwise they just blow it off. It turns out that's really expensive though, e.g. California pays $128k/prisoner/year. Now you're going to have them do some kind of menial labor with a value of what, $10k/year or less? You're still >$100k/year in the red, which has to be less than the per-person inconvenience of having them out in the world. It also costs a lot more than building homeless shelters. It even costs more than mental health services and welfare programs, neither of which are cheap. It is quite possibly the most expensive option that anyone regularly proposes.