Or just continue raising interest rates. At least where I live, the majority of the excess demand during the pandemic came from investors. It was easy to leverage up and buy more houses using home equity loans while interest rates were low and home prices were appreciating rapidly. Higher interest rates should in theory pop all of these asset bubbles we're seeing.
Housing is not free to build, though. I agree in general that more housing should be built, but it's not some sort of silver bullet.
It's usually seen as immoral to bring up in this context, but if you can't increase the denominator, you can try to decrease the numerator.
It's fairly cheap to build if you're allowed to build, though. The issue is all the paperwork.