I don't think many people are really in favor of big investors getting into housing because no, it sure does not help, but the root cause is "not enough homes",

I don't think many people are really in favor of big investors getting into housing because no, it sure does not help, but the root cause is "not enough homes", and the solution is "build more homes of all shapes and sizes". That's also the solution to keeping big investors out! Big investors aren't piling into used cars despite the recent scarcity because they know that sooner or later the car companies are going to go back to churning out a bunch of new cars. You're quite correct that more money chasing after the same limited number of homes is just going to drive up prices.