Anonymity on the Bitcoin mixer platform makes it difficult for authorities to track down people who act as money launderers from hackers or corruptors. Of course the government cannot stay silent. There may be times when KYC is needed for large transactions as a solution to the anonymity problem for security.
That's certainly true, mate. Based on this perception, we could say that Bitcoin mixers are a double-edged sword. It can be used for both good and bad things. Criminals will always look for ways to launder their money, and Bitcoin mixers prove to be the ideal solution for them. However, this privacy technique is also convenient for preserving people's privacy among transactions made on the Bitcoin blockchain from prying eyes. Still, the government doesn't seem to understand this, as it's mostly concerned about the negative implications related to Bitcoin mixing services.
Considering that centralized mixers don't comply with KYC/AML laws, they'll be easily targeted by governments worldwide. If these services want to continue their operations, then I guess that they'll have to implement KYC in the same way as Shapeshift did. Only then, governments will be able to open the path for centralized mixers as they require identity verification for every individual using them.
Despite this, the only way to achieve full-fledged privacy would be towards the decentralized route. Non-custodial mixing solutions would prove to be the ideal solution against oppressive governments worldwide. Slowly but surely, this is being implemented, where people have a choice to preserve their privacy without the need to comply with KYC. With CoinJoin-enabled wallets (like Wasabi and Samourai), CashShuffle (for Bitcoin Cash), and even TumbleBit, it'll be possible to mix your coins in the most decentralized way possible effectively removing the middleman.
Nonetheless, time will tell us whenever crypto will truly stand against restrictive governments for a long time. So far, they've done everything within their power to stop this revolution from happening within the mainstream world. But, their success will depend on how many people will allow them to take control of the decentralized realm. By the looks of it, most crypto services are largely centralized which is considered something bad as it enables a single point of failure (making these services easy targets for governments worldwide). Hopefully, more decentralized solutions would appear that would counteract the effects of restrictive regulations worldwide. Just my thoughts