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?
No, you can still be traced since the connection between wallet hop is not disrupted, unless you mixed your coins using mixing service. Since the process in mixing service is that the BTC send to your address came from another address and not the one that you use to send your Bitcoin.