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.
First, sale is monitored NOT only on the Korean exchanges. I am using bittrex and I haven't withdrawn any money from my account so far, but I did get notifications that to do that I would be asked to provide full information on my real name, origin and date of birth. Secondly, South Korean exchanges are actually quite a big part of all the trading volume there is. It is hard to count it, but I would say that they have about 10% of the top coins' trading volume. That is not too big, but big enough to draw attention and lead others to panic selling for quite some time.