Freedom of movement between municipalities makes most attempts at solving homelessness difficult if not impossible. NY simply shipped them out; cities with nice climates and access to welfare see a large influx from elsewhere. The harder a city works to solve the problem, the bigger the problem becomes.

A friend's mother- a chronic drug user who lived off of welfare- moves from state to state as she uses up whatever benefits they offer.

Not all people are in that situation or abuse the system like that, of course, but small countries with tighter borders have a much easier time dealing with a less mobile population of homeless and indigent.