that after a certain amount of time the bitcoin becomes practically anonymous? As in, not being able to be traced back to the original KYC exchange, or in the case of "tainted" bitcoin, that?
It will be traced back to not just the KYC address but even to all address but the only thing is it will take just some few more time depending on how many addresses it was dispersed or send to. 4 recipient addresses will be easier to 100 and so on. As for exchanges there even exchanges that confiscate tainted coins sometimes that is why it is not even advised to send mixer coins from tumblers or mixers straight to exchanges.
Using privacy like mixers and conjoin services are good because it would at least slow down the tracking process. They promote privacy because it will take a quality advanced tracing algorithms to track the movement of the funds. But I don't need to be scared if mixing coins will be appropriate as much as my coins are from a source clean. One of the biggest misconceptions about mixing and conjoin services is that they are mostly used for money laundering, illegal narcotics, computer fraud, and identity theft. But is this is far from the truth. I just learnt about the output and input principle of using mixers and it became clear that it is important to keep learning in this community.