Your tough-guy jingoism also just ignores all the evidence that shows that just punishing people at the lowest end of society simply doesn’t work. Send them to jail (which costs more than college) and they don’t get out and say “oh, now I have the skills to get my life back in order”.
Being homeless is terribly uncomfortable and punishing already. Nobody who operates on your simplistic sticks-and-no-carrots approach would ever be homeless in the first place.