This means there's a financial incentive for any given city to treat the homeless like shit. Classic free rider problem; why not let other cities deal with helping them?
If you look at the countries where they do a better job, what you largely see is not a handful of metros doing their part, while other cities and the national government completely shunt the responsibility. The whole country contributes, is at least sort of on the same page. At least, that's been my experience living in Germany and reading about other places.
So in my opinion, what we'd need to see is a federal mandate that doesn't let some cities mooch off of others' charity. But short of Bernie storming the white House and the Dems getting an overwhelming majority in both halves of Congress, it's hard to see that happening.
Anyway, I don't disagree that more liberal cities could do more, but at the same time I don't think the problem is solvable without national involvement.