Buying a house is not that easy. You need a bank to approve your mortgage, plus pay upfront money (plus pay for furniture and such) that people might not have because high rent prices stop them from saving money. More renters and less buyers might cause more wealthy people entering the market for speculation, compensating the decrease of people that want to buy to live. And on the other hand, given that housing is a necessity and not something that people can live without, landlords can still push prices up even with increased offer.
In general, I see a lot of takes on the housing market that focus too much on the theory and forgets the reality: people need houses, moving is not easy nor cheap, speculators and realtors can push prices up without that much pressure, and a lot of people don't have enough to face the expenses of buying a house.
This might be true if one could get as cheap and deep leverage on alternative investments as a house mortgage.
Side note: It's heartening that the HN community has evolved in the last 10 years -- the current top comments wouldn't have been at the top 10 years ago, or even 5 years ago. While I think there is still a long way to go, it has come far from almost unbridled worship of PG, libertarianism and "meritocracy".
(It would be different if the wealthy were buying these houses to live in them or to leave them empty, as that would increase demand and constrain supply. Happening in London, Vancouver and a bunch of other places, I think. Also sort of like what happened with the quinoa fad: https://en.wikipedia.org/wiki/Quinoa#Effects_of_rising_deman...)