“The wealthy and corporations” have choices of how to invest their money. If housing supply is sufficiently elastic to meet demand, they’ll find somewhere else other than housing to put their money. Ain’t nobody trying to corner the Chinese real estate market in 2024, for instance (*).
There are a few places where land shortages genuinely constrain housing supply, like Singapore and Hong Kong. But the US has tons of land; things are simply not well optimized. That, plus high interest rates due to fiscal/monetary mismanagement.
(*) Not saying the Chinese real estate market is worth emulating.