I always felt like this was kind of obvious. People love to say housing supply will lower prices, and it's probably slightly true, but it's fairly clear that house prices go up in places that people have money, and they go up proportional to the money. In the US the rich have comically more money than the poor--100s or 1000s of times as much, comparing the surplus that a wealthy tech employee has to put towards a house fund compared to a person living paycheck to paycheck. And then the rich will then buy vacation homes, pied-a-terres, etc, with their huge excess. Who would put money into building for people who have no money when those people are out there?

Rent on the other hand is likely more supply/demand based because it is actually possible to have empty units due to overbuilding if the local economy shifts. But even still they are motivated to hold units empty and keep the price high to wait for a rich person who can afford it to come along. (Not to mention algorithmically colluding so as to not actually compete on price.)

I cannot imagine how housing could ever become more affordable for the poor unless the income disparity lowers, short of some sort of price-fixing governmental action.