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.