I live in Manhattan, and one thing I've noticed is that panhandlers are generally polite and unobtrusive, and other homeless nearly invisible. I'm sure that's the result of aggressive policing -- a spoken but unofficial "don't hassle anyone and we won't find an excuse to bring you in." Maybe the answer is to minimize the negative effects of homelessness as much as possible without attempting to "eradicate" it?

Bear in mind that obviously I only know this equation from the middle-class white-collar side; for all I know, the lives of the Manhattan homeless are no better than in cities where they could be more rambunctious.