Yes, if every single rich person owns a flat in NYC, that might make NYC unaffordable. They might also do the same in London and SF. That only leaves the entire

Yes, if every single rich person owns a flat in NYC, that might make NYC unaffordable. They might also do the same in London and SF. That only leaves the entire rest of the world to live in. If the rich concentrate, they can only harm a small number of locations. After all, there aren't very many of them. Then there's considerations for housing growth - as inequality and population rise, housing demand increases, but ability to pay for that housing does not, so why would you expect any additional to be built, given the increased cost of the land due to the increased demand for that land? Well, I'd expect additional housing to be built because developers are clamoring to do exactly that. They are just not legally permitted to do so in a few of the highly desirable locations (e.g. NYC, SF, Paris).