As wonderful as this idea is, I have a weird conundrum with it. If a solution to homelessness is to give people homes, we already have enough vacant housing to do this. In fact, for every homeless person, comparing their numbers to the available houses, there's actually a large enough volume of homes that the homeless quite literally can pick and choose where to go.
That said, helping the homeless needs to go beyond just homes. They, first and foremost, need to be treated as human beings and not some sort of plague. As someone who used to live in New York, it's profoundly dark to see how normal it was for people to just walk by the homeless as if they were no different than trash in the street. The way we normalize the plight of others is of issue too, as we blame people as if they exist in bubbles, failing to realize in many cases, especially today, it's systemic. There is a lot that goes into poverty today and homelessness, and that starts with an expansion of precarious conditions.
Homeless people will also need help with addictions, mental health, assuring access to baseline needs, the works. We must not ever forget those things and understand a home is a foundation, a type of "ground zero" for their wellbeing, and whatever we can do there, we should. If we give them a home and no other aid, the home simply becomes the place where their problems fester. We must fully "cleanse the pallet" as it were.