These skyscrapers buy "air rights" from neighbours to build high which takes away even more homes.
London has areas with the same problem.
Places like NYC and London fit a kind of niche where there is a market for this sort of opulence/money-laundering. But if you, like, sit on a bunch of commercial real estate in Des Moines Iowa, turning it around into a $50 million apartment for the Saudis is not a real possibility.
The rest is basically irrelevant. Every one of those few "billionaire" buildings could be 1-bedroom market rate units at 100% occupancy instead and it wouldn't do anything significant for the overall problem.
For one example of how broken NYC policies are: 60% of residential lots aren't zoned for anything over 2 stories. The city needs to have much of it moderately upzoned to get decent (and decently distributed) housing development, not to somehow start building affordable skyscrapers in Midtown.
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There's a fantastic non-partisan report here that lays out the scale of the failure and various ways to improve the issue very clearly: https://cbcny.org/research/strategies-boost-housing-producti...
If you want to just skim, the various charts show it clearly enough without actually reading every paragraph.