Or, seeing as how it's kind of important, we could subsidize building more housing.
(There is an article here on hackers news not too long ago that said that while most industries had had huge productivity gains in the last 30 years, construction had been flat or decreasing - mostly because of increased regulation)
Permits for everything (some permits are good, some are SO bad), mandates for things that increase cost for marginal/no gains in the finished product, and a ton of red tape/money going to people not involved in the actual work or the quality of the end product. If I, as a builder, have to go through all that bullshit for each house I build, the sane response is that I'm only building expensive houses that take more time but end up being similar $/hr for me, because I end up saving money and time dealing with the regulators.
NIMBY policies have broken the traditional boom and bust cycles of housing in California that used to ensure there was enough housing for everyone.
It used to be that when demand was outrageously high, it'd start a housing boom where builders would start reinvesting profits from building higher-end places into building more and more until they'd overbuilt. Wealthier people would move to newer places freeing up stock for everyone else. During the bust, you'd have even more people upgrading as prices reset.
LA seems to be experimenting with suspending some of the anti-building policies which is certainly good, but they're still stuck on this idea that it should only be for below market-rate housing - as if the laws of supply and demand don't exist.