Unfortunately, for centralized mixers at least, you're wrong. In the US, you're prohibited to run a non-regulated money transmitting service; and that's pretty much what a good Bitcoin mixer is. Anonymous and it involves and intermediary who will transmit money. However, that does not apply on every country, and it does not mean decentralized mixing is illegal.
If centralized mixers should follow the Bank Secrecy Act and register as a money transmitter, they have to follow anti-money laundering and know-your-customer compliance commitments. But is that possible? If they follow it, that means they are no more mixers but another thing else.
Just like I said, gambling is not legalized in all countries in the world. Cryptocurrencies are not legalized in a countries of the world, there are over 10 countries in the world that completely ban cryptocurrencies. Because something is not legal in one country, that does not mean it is not illegal in another country.
We can just take it that mixers are not completely illegal. But if they see it having illegal mixing, there is possibility that it would be taking down.