Not sure it's so magical. If you own a home in a city whose GDP is increasing every year it makes some sense that property in that city would also increase in value.
The reason people aren't buying a home in cash, which is not necessarily common but completely doable and not illegal or anything, is because almost no one can afford to do so. Saving for 30 years and then buying a house in cash all while paying rent somewhere in the meantime I think is pretty undesirable.
You're playing semantics. If there aren't physically enough homes in NYC for the number of interested buyers there is Scarcity. Talking about that source of that scarcity is irrelevant. Re-Zoning fixes nothing in the short term and scarcity will remain. Even if you re-zoned you need to physically build up inventory which takes years.
Seems like an easy thing to test, just adjust for income in single parents and compare outcomes. Easy enough that it's likely been done before and didn't materially change the outcomes of this kind of analysis