> since homeless will often migrate to where the functional support services are.

I've heard this a lot but I don't have any reason to believe it's true. Never seen a reputable study that asserts it. I've known a lot of homeless people but none that relocated for this reason. Most who moved were looking for work or trying to get closer to family. Most didn't move at all and were just where they had always been, or in the city they were living in when they became homeless.