> City's deal with their homeless populations in different ways, but if any city is overly generous it quickly gets swamped. Further, cities can export their homeless by being overly draconian.

I doubt the issue is as simple as I believe you intend - I don't think there are many examples of draconian cities eliminating homelessness via exports. I also don't think overly generous cities are swamped as much as you believe - size of city & climate are larger factors in homeless population size than generosity.