This is not even close to true. It’s regularly recognized that for many people, homelessness is rooted in disabilities, mental health issues, substance abuse issues, or other problems that hurt their ability to keep and maintain a home even if they had one.
It’s not at all a pure supply issue, although supply plays a big role in certain geographic areas. It’s a complex problem.
Keep in mind that even if you own a home, maintenance, utilities, and taxes are expensive.
Regarding substance abuse for example: Shall I happen to lose my home, I would have to use the named substances to soothe a terrible shame and misery associated with my new status. I could only think of fighting my harmful addictions if I can see the way out. Currently though, with number of houses almost constant, if you manage to pull a homeless person out of the streets, there will be another person priced out of their home.
As we all know, N_homeless = N_people - N_homes.
Current regulations effectively forbid to build horrible ugly high-rises that can house 50,000 people in each. Currently, it is only profitable to build luxury houses that nobody can afford.
However, the horrible ugly high-rise has the only one advantage: it is cheap, and everyone can afford it. Even a homeless guy that manage to found a crappy -paying job through his heroic effort.
I only see one way to end homelessness: make housing 20x cheaper than it is now. And that would not be possible without cancelling all housing regulations.