Like another comment here mentioned, housing is complicated. People don't want to live in a random house in the middle of nowhere ('roof over your head'). Some people prefer to be homeless on the street versus getting to a roof over their head that they don't like. People want to live where they want to live (near family, jobs, culture etc) Take NYC for instance. Politicians try to address the NYC housing crisis from…
It looks like you can't see the real issue: too many people want to live in NYC. If you make it cheaper to own, build or rent in NYC even more people will come and the there will not be enough housing. Perhaps people should be encouraged to live somewhere else/in more places? Living in NYC is not a human right either.
When you take a look at Tokyo, who have had stable housing prices, and have a sane zoning system, what you see is that people can live where they want to live. Yes you have some skyscrapers. But you also have many places that aren't.