I'd happily donate to a homeless person who was actively cleaning the street, for example. But for some reason people seem to prefer deciding who to blame rather than proposing solutions.
We refuse to do this out of nebulous concern for individual freedom (political left, libertarian) and economic incentives (political right, libertarian), no matter that persistent homeless have mental health problems (acute or non-clinical) that are contradictory to simplistic notions of individual liberty and individual accountability. (Because the real concern is the hypothetical liberty and accountability of people who otherwise would never have trouble staying housed, not those rotting on the street.)
Saying "Either take your free room, or get your own room, or leave the city, or as a last resort get committed." doesn't strike me as particularly bad as far as freedom goes.