If houses were just a commodity to be bought and sold we'd have much less of a problem. There were very few homeless a hundred years ago. Efforts to ban residential hotels aka "flophouses" were mostly an effort to remove undesirable people from their communities by making it impossible for them to find housing there they could afford. And the fact that many if not most voters don't want housing for what they consider undesirables in their neighborhoods is a huge problem for the construction of homeless shelters and affordable housing to this day. So I don't think that even completely socializing housing would do all that much to help with the problem.
