They're going to bring in laws for regulated exchanges but American law won't be the same as New Zealand or Mongolia. It's going to be about the country you're living so laws are going to be different. In time trying to keep some crypto swaps private's going to get restricted so we're going to lose more privacy.
Governments are increasing their surveillance efforts with the excuse of preventing (or minimizing) as much criminal activity (money laundering, tax evasion, terrorist financing) as possible. But we all know their real intentions. They will ultimately abolish privacy/anonymization techniques to prevent people from getting true financial freedom. Only government officials and bankers will be able to achieve privacy.
Even though governments won't be able to shut down decentralized mixers, most people won't dare to use something that's "banned" from mainstream use. Those who are caught mixing "behind the scenes", will either face fines or jail time. It's a dark future we're heading into. So prepare yourself for the worst.