If the free market were one entity that could coordinate and say "nobody build more housing, let's squeeze as much money from what we have already", sure, that would be pretty profitable. But if there are enough participants in the marketplace (which depends on the barriers to entry to homebuilding, like regulatory capture, knowledge, capital, and permits) one will want to undercut the others and build houses marginally cheaper than the competition until their marginal profit is zero. Having everyone agree not to build houses and keep prices high is like the "nobody snitch" outcome of a prisoner's dilemma: it's not a stable state/Nash equilibrium. At least this is what I heard in Econ 101, I'm sure I'm missing much nuance here.