There has just never been much reason to believe that supply constraints were the primary driver of housing price increases. If they were people would have moved, or somewhere would have ended up being a lot better.
It used to be that housing costs tracked incomes. If you had a medium to high salary you had decent housing. Since the 90s with urbanisation and increased wealth not only do more people want to live in the same places but some have a lot more to invest. So you now need high wealth to have decent housing.
What many really want is housing below market rate so they either don't have to work thier entire lives or can also become wealthy, and preferably both. Which is understandable but not realistic.
Anyone who doesn't believe this should note that this has already been discussed on HN for at least 10 years and still hasn't been solved anywhere I know of globally. But instead still roughly tracks local wealth (and income). And will likely continue to do so.
Because that is what the housing market does. Allocates valuable assets to those who pay the most. Nowhere on the tin does it also say that it promotes social mobility or equality. Maybe it should, but it certainly won't as long as there is the idea that it already does.
That said, is there some effect of supply constraints? Sure. But ultimately it would increase urbanisation, making the situation worse. Affordable housing is already available on the market. Just in places with lesser jobs and living conditions. Which again it is understandable that many don't want to live in. But it isn't a market issue.