States can certainly control the behavior of ordinary businesses that operate in their borders. Maybe they can't directly stop some hacker somewhere from operating a mixer but if coins from a mixer are as illegal as coins from some crime, these businesses won't want to touch.

I mean, the FBI has already shown it can see through mixers and arrest those who try to cash stolen bitcoins.

China has made sale or possession of bitcoin a crime but the West is following different road - with enough state intervention, bitcoin will wind-up a public money, less private money system than regular bank accounts. Every transaction is on the blockchain and that is public. Try putting that in your "anarcho-capitalist" pipe and smoking it.