Yes, building houses actually solves homelessness. Housing prices are the best predictor of homelessness and of course increasing supply of a good decreases its price. Why does the law of supply and demand not apply to housing? Sometimes the solution is very very simple and not at all complicated. Just build more.
> Why does the law of supply and demand not apply to housing?
Who said it doesn't? How well do you understand the law of supply and demand when you don't know what a price floor is? Ignoring that, do you think someone on the street can afford even a $1000 home? That's before we set aside that this of course only works if the houses being built are being done in a way that actively encourages prices to go down, rather than feed real estate speculation and continue to float a culture that sees a home as a capital asset.
So no. Building houses alone does not solve homelessness, again as evidenced by the fact that houses are built all the time in America, and homelessness is not getting better. How did you miss that?