Yes, but what if you own 100 houses? I'm pretty sure there is some number N of houses (or total value of houses) where I would be fine telling the person, "You don't get to decide what to do with these houses anymore, they're going to be given to people who need houses." Not as a matter of antitrust or monopoly but just directly as a matter of an individual controlling too much wealth.
Aside from that, once you admit that there can be restrictions on property rights, it's unclear how property rights in and of themselves is a steelman of private equity. Why not just say that "you can't sell to private equity" is one of the restrictions? Or, perhaps more subtly, why not say that a private equity company of a certain size is not allowed to buy any additional company, independent of what rights that company's owner has to sell?
Aside from that, once you admit that there can be restrictions on property rights, it's unclear how property rights in and of themselves is a steelman of private equity. Why not just say that "you can't sell to private equity" is one of the restrictions? Or, perhaps more subtly, why not say that a private equity company of a certain size is not allowed to buy any additional company, independent of what rights that company's owner has to sell?