I can imagine many governments regulating them the same as exchanges, forcing them to do KYC/AML and what not. They can then prosecute the operators in their countries that don't comply, exactly like exchanges.
Banning coins they can try, but hardly succeed. This time its a decentralized service which is not easy to shutdown. Centralized services like exchanges and mixers could be attacked. Well, unless there is some decentralized mixer out there, which should be possible to do (and easier than the
Bisq DEX).
Without a doubt, governments will try their best in order to stop people from using privacy services at all costs. They've successfully shut down Bestmixer because it was a centralized service. Imagine what they could do with the rest of Bitcoin mixers available today. That's why, it's best for these services to remain in the most decentralized way possible in order to prevent third-parties from taking any action against them. Luckily, we have non-custodial wallets for Bitcoin that use CoinJoin anonymization techniques like Wasabi and Samourai. On the other hand, we have a decentralized mixing service called "CoinShuffle" available exclusively for Bitcoin Cash.
Which is why, the more decentralized mixing services appear, the better for the people. I believe that it's time for individuals to take back their privacy via the use of a cryptocurrency like Bitcoin and various anonymization techniques available today. With this, governments won't be able to stop every privacy service, effectively eliminating the middleman as Satoshi originally intended. I believe that current centralized mixing services will have a hard time with worldwide governments as they impose KYC/AML regulations. Even instant exchanges like Shapeshift, turned out to require KYC after so much pressure from the government.
Nonetheless, governments may consider mixing services illegal, but those which are decentralized will truly prevail in the long run. People will always look for alternative ways to get access to this, especially when it comes to their privacy among Bitcoin transactions. In the end, governments will recognize that their efforts will be in vain, greatly joining the decentralized crypto revolution in the long run. Just my thoughts