The cities that have had less crushing affordability problems are the ones that have been able to continue expanding outward - the outskirts land that used to be empty now has housing (and got more valuable as a result of this development) and the inner areas (slowly) has been getting denser, especially as old industrial property gets redeveloped and such. But many of those cities have just as much zoning and restrictions around density as NY or SF (usually more!). The difference is that they were able to go outward to better keep up with demand increases. I don't think any US city has been able to address rapidly rising demand through upzoning and density alone - redevelopment of existing residential will always be much harder and slower than of empty perimeter land. Density, on the other hand, has seemed to ultimately cause demand increases in NYC and SF greater than the supply increases it has provided.
If population growth stops, though... all this changes. Or even if just the net migration to various cities shifts around!