> They are expensive largely because of housing so your statement is a bit of a tautology.

Yes. And that's impossible to fix.

> Historically NYC housing used to be a lot more affordable before they stopped building, reducing supply relative to demand and thereby raising prices.

Demand will _always_ outstrip supply. And there's no such thing as "affordable housing", it's a contradiction like "hot liquid helium". If housing sells, then it's affordable for _somebody_.

What you're talking about is subsidized housing in some form. Like rent control or housing projects.