Coin mixing is unavoidable, however this will make bitcoin more and more like cash, thus result in the same restrict applied to cash from financial regulation bodies today
And how are they going to put restrictions over coin mixing specifically? It's pretty much impossible to stop. If they try to ban mixing services, there will be tor based alternatives all over the place anyway.
Also, any exchange can act as a mixer. If you leave your coins in a exchange for some days and withdraw in small lots its a mess for anyone that wants to tax you or something.
They can not restrict mixing, but they can restrict the entry and exit from fiat money system, thus apply similar rules like cash: you have daily/monthly withdraw limit from exchanges, and large amount of bitcoin transaction to exchanges are not allowed
Even if you can spend directly at merchant's place, regulators just need to regulate all the merchants and give them a daily/monthly purchase limit for every consumer. Large bitcoin transactions are prohibited just like large cash transactions are prohibited now. If you want to do large bitcoin transactions to exchange fiat money/purchase something, you have to use government registered bitcoin addresses, like a formal bank account. And business maybe all required to register their bitcoin addresses
In this way, they can also get rid of the tax headache, actually government can not tax cash transactions easily, but due to those transactions are small, government don't allocate resources to chase those tiny tax income, they chase large enterprises for at least millions worth of transactions
