The idea of homeless people as rootless resource consumers free and willing to migrate any distance for services is completely alien to the actual experiences and issues.

Almost half of homeless people have jobs. The "street homeless" are the visible tip of the iceberg but not representative. And even more importantly, almost all homeless people have family and friends, churches, AA meetings, coffee shops where they are welcome on rainy days, etc. These ties are just as important to them as they are to you, and they are just as reluctant to break them as you would be.

Surely people do move only for better access to services but I have never seen numbers on how many. More interestingly, in years of my own homelessness and later ties to those communities, I never met one who had.