China serves as this counter factual and it's facing an even larger housing crisis. Massive building of houses lead to many people buying up property for investment reasons and now there is a pretty clear oversupply while plenty of people still struggle to find housing.
I don't really understand why HN is obsessed with building unlimited housing as though this will fix the problem. For years people clamored that this was the solution to all of SFs problems, but as SF starts to shrink it already looks deserted, I can't image what happen if the HN fantasy of building unlimited massive apartment housing had materialized.