The hedge fund thing is way overblown. Even if they buy up homes in hot markets, their incentive is still going to be to sell them if/when the market cools. Corporations do not enjoy the same tax incentives as homeowners in this country, and the risks/costs to rent out older homes just doesn't pen out for non-local investors. If PE wants to get into housing, it's such a better deal for them to just build apartments.
Currently less than a percent of homes are owned by private equity. And the majority of those are owned for the purpose of turning around and selling them, like Home Partners.
(Zillow also tried buying up homes for the purpose of arbitrage and it ended up blowing up in their face).