I'm not sure I completely agree with that.
Suppose you wanted to build the maximum amount of free housing as quickly as possible. What would you do?
You'd pick someplace rural (where land is cheap, and there are fewer people to raise objections), buy a bunch of land and just build the homes (and services needed by the people who would live in them). You would then invite anyone who needed shelter to come live there for free.
But if you actually try to do that, "homeless advocates" will say all sorts of mean things about you and block the project. So I would argue that not everyone wants the solution of just building enough homes for everyone.
They want homes built in specific places, and those specific places happen to be highly desirable and very expensive places to build acquire land and build homes.