Except it simply doesn't work that way in the real world, and there are tremendous number of homeless people in Florida and virtually every other brutally homeless-hostile locale. People aren't trivially mobile -- especially if their lives are insecure and moving would mean losing the one or two connections or lifelines or familiar surroundings they have. Some have physical or mental difficulties that prevent them from relocating.

They aren't perfectly mobile, but over time a city that's welcoming to the homeless will attract more homeless people than cities who are actively hostile to them, particularly when cities are willing to buy bus tickets to get homeless out. Sure, not everyone will move, but some might, and when there's a disparity in how homeless are treated for years and years that adds up.