[anonymous_sorry]

More very rich people looking for somewhere to park their money and earn returns means more competition when you want to buy a home.

I agree it doesn't necessarily mean rents rises. You might actually expect higher price to earnings ratio with more wealthy people competing to buy assets (see also stocks).

But it will lead to the shrinking of the home-owning middle class.

That's not to say there isn't also a problem with lack of supply.