There are a plenty of people who want to build more housing, and they would make a lot of money doing that if it wasn't illegal. The problem is not capitalism, it's statism.
It's an infinite loop. Build more housing to suck in more jobs and people. Then you need even more housing since people from now-depleted surroundings come in. Rinse and repeat.
It's not capitalism or statism. It's lack of safeguards to prevent concentrating too many people and economy into too tiny pieces of land.
And housing problem exists in places other than USA, with wildly different policies.