I'd suggest that a solution to the demand problem is basic income. Let those who can and want to move out to the sticks and live on UBI. There are a nearly unlimited number of places with low cost of living and ample or potentially ample housing. Why does everyone want to move to SF and NY? It's not the poop on the sidewalk, it's mostly the jobs. Fewer people having to move to big cities for work (especially those who prefer the country) means less housing pressure.

I think UBI would significantly help relieve housing pressure in large metro areas and perhaps help revitalize some currently-dying small towns and rural areas, which after all will need more services with increased population.