>Or you can rent that house after the PE firm buys it and rents it out...
That's fine? It's still contributing to the housing supply, it's not like they're hoarding the houses. Moreover unless you want to ban rentals entirely, you're going by definition need people owning more than one house. Finally, the fact that rents are sky-high as well, suggests that housing is expensive in general, not only home ownership.
Homeownership is one of the main ways that Americans transfer wealth, as it's usually the only asset that adults nowadays have that can be transferred outside of whatever's in their bank accounts.
When homeownership becomes restricted due to PE firms and Investment firms buying up entire communities to turn into rentals, the wealth transfer is hampered. Well-off adults are still having to rent and are now directly competing with younger Americans who are still growing in their careers and pay scale.
This puts older Americans in a tough spot of not being able to generate wealth or equity that can be transferred to their children. And this puts their children and younger Americans in a spot where they cannot afford to live where they work, and cannot afford to save enough to begin the journey to homeownership. And the promise of a wealth windfall when their parents pass is becoming less and less common.
What is worse the PE firms can collude (internally and/or externally) to withhold units for rent to influence prices once they capture enough of the market.
Constructing new buildings would be contributing to the housing supply.
Buying an existing home, so long as it's rented out is yes technically providing housing supply, but it is unhelpful rent seeking.
That big investors would rather buy up existing homes rather than invest in building new ones is a pretty clear sign that the housing system is dysfunctional and requires work on the taxation/regulation side that would encourage more productive use of investor dollars.
I believe the correct response here is "That's wonderful! It lets everyone get in on the benefit of being a slumlord without the hassle of shaking down your tenants. Now you can just buy shares in this instead!"
That's fine? It's still contributing to the housing supply, it's not like they're hoarding the houses. Moreover unless you want to ban rentals entirely, you're going by definition need people owning more than one house. Finally, the fact that rents are sky-high as well, suggests that housing is expensive in general, not only home ownership.