> I believe that if you increase supply and allow more affordable housing in a city, it will only marginally decrease prices but will mainly attract more people to this city.

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?

Prices are set at the margin, and demand is largely driven by employment.

> 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.

Having higher local taxes in major cities would just expand the problem. The poor and middle class will get further pushed out, and the rich who can afford the tax and prefer living in the city will stay, in which case you just get SF all over again.

NYC has substantially higher taxes than most of its suburbs. It also has a much higher draw due to its dense population supporting fancy bars, arts, and other world class amenities. The network effects of living close to other interesting, cosmopolitan, or just niche social group people are also valuable.

At some point you run out of people that can move into the city... which might make the city huge, but eventually supply will outstrip demand.

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.