Even if this change from Wasabi won't affect any of your inputs, they are no longer an entity which I can trust to fight for my privacy.
Would it be possible for some to start running coordinators?
Absolutely. The coordinator code is open source, so anyone can download it and spin up their own instance. That would solve the immediate problem if everyone switched to a different coordinator, but it doesn't stop these other coordinators being pressured in to implementing the same restrictions and it doesn't change the fact that Wasabi did this in the first place instead of fighting against it.
In fact, they need to cooperate with blockchain analysis to obtain information about "taint" UTXOs.
Well, they only need to cooperate in this sense to have the blockchain analysis entity feed them data about which UTXO's to block. But as I said, if they cooperate like this then it won't be long before that cooperation becomes a two way street, with them feeding data back to the blockchain analysis entity.