While Blackstone and other PE firms are involved in buying those assets directly (part of my old job), Blackrock is also indirectly involved by buying up massive portions of the REITs listed by these firms, which validated the business in the first place. Without the extremely insane amounts of money pumped by Blackrock, Vanguard and State Street into these structures, all for some measly 4-5% return (laughable for most sophisticated investors but apparently good enough for these guys), they were able to put the accelerant to the fire. Neither BX nor any other PE firm would be doing this model if a market didn't exist for it.

While I'm obviously biased here, imo Blackstone is much better still because you don't see Steve Schwarzman go around pontificating while using the voting rights of passive investors to force certain behaviors upon the boards of nearly every company.