~snip~
However, the buyers do not actually control the BTC, it is still in custody of Blackrock. And no amount of BTC in your custody gives you any mining power. That only happens with Proof of Stake like Ethereum.
As far as I know, BR and most companies that provide spot ETFs services use external companies to store the coins they buy for their clients. In that sense, neither their clients nor they have complete control over those coins - and in fact both can hope that whoever is holding them won't be hacked.
However, with the beginning of offering BTC ETFs, BR started buying large shares in mining companies, so it may seem to some that they are trying to gain some kind of control - especially if we know that their official position is that in the case of a hard fork, they will not necessarily follow the chain that will be supported by the community.
Of course, all of this leaves a lot of room for speculation, but one thing is certain - they and the like have no sympathy for BTC except to extract as much profit as possible from all this.