but each user (payer) can be objective about the provider which is censoring their own transaction. And since they all move away from that provider to avoid the censorship, then it has the net effect of taking PoW hashrate away from that provider
This objectivity is fine, except for the fact that the attacker is free to create an overwhelming majority of providers, such that moving away from one to another has no effect at all. There is a sybil problem here. You can attempt to mitigate this by making it expensive to become a provider, but then we regress back to the PoS security model, which no one wants in a new coin.