If the supply of houses were not artificially constrained, their price would not go up like crazy, and Blackrock would simply not invest. They don't like to invest in things that don't appreciate in value. The fact that their buying drives the price up could be superficially perceived as a win-win for them. In reality, whenever someone is large enough so that their buying of a thing drives up the price of said thing, a roundtrip (first buy, then sell) generally leaves them poorer overall.
It’s a downside for the many of capital concentration by the few. Basic necessities look attractive, money like that needs someplace to go, according to its owners. Wait until tap water is mostly owned by private capital.