Yes but it also has a pretty long lead time so continued mass immigration always drives up the price. It's true of most hard infrastructure.

It's mostly due to absurdly difficult to get permits.

A benefactor decided to solve the housing crisis, created a development company. Gave up 2 years later. Stating the legal burden to get permits was the biggest financial obstacle. We are ready to build from the start, 2 years later we still couldn't build and spend most of our capital in lawyers in hope to get any approval.

Which makes cutting back on immigration a short term solution.

Population growth is driven largely by immigration though.

And what do you suppose drives the growth in housing?

I mean, if the goal is fewer people, then there are many many nefarious ways to achieve that.

Really with birthrates the way they are going, unless radical life extension comes soon it's going to be a problem that "solves itself".

We could also just do a good ol' fashioned culling!