Nobody can do that at protocol level (lessen our anonymity or privacy in transactions). All they can do is to regulate centralized services like exchanges. Bitcoin is like cash. When you go to a super market and buy something and pay in cash, the owner doesn't ask you for your identity to make the payment but when you use a centralized service like banks (eg. debit/credit card) you have already revealed your identity.
It's the same with Bitcoin. People don't want their privacy be invaded, then they shouldn't use centralized services with their decentralized money called bitcoin.
This going to change and grow over "exchanges". We already have supercenters / super stores in here, that only accept max €200 cash money, because they are complying with new upcoming AML regulations. Same will happen with bitcoin when it will be tried to use as a cash.
You might not be able to control bitcoin in protocol level, but you can already see what happens when people try to play that card. What do you think will happen to your btc when it goes trough the mixer? Because you might get away with that with small amounts, but as laundering that gets trickier, people might reject it as a payment, because they won't want to get involved. It will be them who will need to explain the source, and it will be their accounts frozen.
they will make it hard to use as payment for anything significant, as you will need to prove the origin of the crypto, and once it touches something illegal, restricted or source is been obfuscated. That crypto will be tainted