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?
If you sending your bitcoins back and forth between different addresses in one wallet, it does not make sense. All transactions will be linked to that wallet. Do you mean back and forth by sending your coins to your used addresses? It is bad because the recommendation is don't reuse your Bitcoin addresses.
If you have ever read guidelines to use Coinjoin transactions or Mixers, you will see they emphasize the importance of Inputs and Outputs. You have to choose Inputs, Outputs and Anonymity set properly to have good anonymity. If after a Coinjoin transaction or mixing process, you use Outputs to send back to your used addresses, it does not help your anonymity.