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, it is still going to be traceable based on the input and output, and that's not how mixing works (as this seems to be your goal in the beginning, based on your definition).
So it's better to just used bitcoin mixing or tumbling services to achieved anonymity. You can find a lot of them here, some of the forum community even carry bitcoin mixing service signature.