This only works if all those houses are on the market. Nothing is stopping today's rich people from buying up all new housing, and only letting a handful be on the market so as to not flood the market and not let prices go down.
What’s stopping rich people from buying up every car in existence and making you pay $1 million for an accord?
Ah, the classic investment strategy of eating up the cost of keeping a house empty, so that others who do accept renters would make more money
”The rich” aren’t that stupid, why would they take the losses to support someone else making a profit?
They do not have enough capital to do that. Housing is such as large market that eventually anyone but the state would run out of capital. And it is not actually even that profitable... There is much better investments.