I don't understand why this would just be a supply-side issue, rather than a huge demand-side issue given asset price inflation consequent from QE, the expansion of private credit and the financialization of housing over recent times. Or indeed a distributional issue given that we are now living in a new Gilded Age, of poverty amidst plenty.

A lot of housing problems result from the uneven and combined development inherent in capitalism. Physical and human capital floods to major sites of economic activity, leading to a positive feedback loop benefitting a small number of major cities. The rest of the country becomes a hinterland, sucked dry of business and anyone who has the option of leaving. In the UK, where I live, this is the major underlying cause of Scottish independence, and now the increasing calls for Welsh independence, and even Northern independence. The economy is asymmetrically built around London. That in turn makes it increasingly difficult for normal people to live in London (e.g. nurses and teachers). Zoning isn't going to fix that.