Homelessness only partially overlaps with what British authorities euphemistically refer to as "street lifestyles". The people you see blacked out in the gutter or ranting wildly on a subway car are disproportionately likely to be homeless, but their behaviour is not the result of homelessness - many of them do in fact have a stable home and most of the rest would continue to behave in an antisocial manner even if they were adequately housed.

The problem of persistent disorderly conduct by a small minority of highly disturbed people is either an unfathomably complex psychiatric issue, or a fairly straightforward carceral issue.