Ok here's what we do. We build a social housing, but we officially call it a "prison." People who are picked up for homelessness-related 'crimes' like public camping can be "sentenced" to this 'prison.' It will officially be a prison, but it will be unique in that every prisoner will qualify for daytime release. It will also be so low-security that there won't be any guards. Still, officially, legally, it will be a prison.
That way the homeless-haters can still masturbate to their hate-porn, but the rest of us can actually get around to solving the problem.