If you offer free housing, a bunch of non-homeless people will apply for it. Many adults live with their parents. If you bought a farm and built a giant apartment complex, they would have homes, but they would be away from support services and jobs. Increasing the population of the exurbs increases the need for roads.

Many people don't despise the homeless; they just want them someplace else. I think that we need to reduce immigration -- both legal and illegal. If you build enough houses for everyone and stop population growth, then you can solve the housing shortage issue. If you increase the population, you have to build both more houses and more roads.