What a clickbait title ! Anonymity is not leaving Bitcoin ! You can still buy your bitcoins with cash and get covered without any problem ! Only sale is monitored on South Korean exchanges, which represent, let me remind you, a very minor part of the world volume.
And some exchanges that implemented the KYC compliance policy, title is a self-explanatory that cryptocurrency is no anonymous yet the Op stated some facts from a country who pulled off some exchanges to support the thread, it is not the coins itself who are not anonymous, you can still perform transactions not just in bitcoin but on any other coins as long as it is not requiring some information anonymously, some multi-platform web wallets and local exchanges already implemented this compliance in order to eliminate abuses.
Even bitcoin itself is pseudo anonymous and obviously, you can still stay anonymous as long as you want to. Like you said, what OP is getting wrong is that this is not about cryptocurrencies but about exchanges.
If government is going to be doing any regulation, that balls down on exchanges and as long as anyone feel they can stay out of exchange, spend their crypto without converting to fiat, which at least for now, unless you are purchasing something from a crypto enthusiast, it is impossible to do. So with that, I guess we are bound to exchanges and regulations.