We don't need to use additional methods to keep bitcoin fungible since the most important and effective of them has been an essential part of the bitcoin network from the very beginning. It's mining. Mining is what makes bitcoin perfectly fungible because even when 'tainted' bitcoin goes through the process of mining and gets added to the block, at least part of it becomes clean again through transaction fees. To keep the political nonsense of taintness sound convincing, governments and other agencies would have to declare all transaction fees illegal since it is not possible to distinguish between legal and illegal coins once they get laundered through fees. They would have to go further and declare the very process of mining illegal because there is no way to control which coins are being laundered.

They can't log mappings between inputs and outputs, however, a malicious coordinator can log ties between unrelated inputs (it can learn which inputs belong to the same user), which is also very useful information for three-letter agencies.