OP is right. The demand is huge and supply is tiny. Even with those scary panhandlers people are jamming onto public transport (when it actually exists) and going far far out of their way to experience walkable areas.
> zero other options if I want to live where crime is low and the schools aren't dysfunctional
Crime in NYC is exceedingly low and the schools are great. Why don't you simply move to Chelsea or the Upper West Side?