I think the solution to housing cost is to make smaller cities, towns and the countryside more attractive by having higher local tax rates in cities. This source of income could be used to build better infrastructure in the rest of the country.
I believe that allowing more units will lower prices, but what if it didn't? What if all that happened is that a whole bunch more people got to live where they want to live, productivity increased, and the largest cities got more dynamic and interesting? What if that's all that happened?
> by having higher local tax rates in cities
You already pay taxes on par with Denmark if you live in NYC and have sufficient income to afford to live there without subsidized housing. Tax policy is an insane way to prop up little towns. Cities offer a lot of economic and environmental benefits, and are generally already generating more tax revenue than they receive in benefits.
Also no thanks to wealth redistribution. The rest of the country sucks outside the coasts sucks and its mostly because they have regressive politics. It's their own damn fault nobody wants to live there.