This would be like opening a can of worms. If they were willing to do that now, who knows at to what extent they would cooperate with authorities in the future? Who is to say that they would just stop at blocking tagged addresses? As mentioned already, imposing KYC level verification is not out of the picture.
This proposal has been brought up before, but from what I know, all Mixers have maintained the existing system without user selection. The protocol doesn't prioritize or prevent anyone, which is perhaps what we've always appreciated when talking about blockchain. The core value of Mixers is their ability to provide maximum anonymity for users, there's no reason for them to harm that core value and then be eliminated from the market.
The gap in this market could be filled by a service, for example, Semi-mixers that apply KYC or cooperate with governments. However, I don't rate their ability to survive and profit highly, they might not even be able to reach potential users in the market.