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?
The best way to stay anonymous with your bitcoin transaction is to make use of the mixing service, it will not allow the linkage of the bitcoin wallet address you're receiving or sending to, the mistake people make is that they thought rebroadcasting of their funds on multiple wallets will make it anonymous to track, but the real idea is that it may increase the difficulty in making the linking but not making it anonymous, the best way to achieve privacy is to make use of bitcoincore software for by running full node transaction on the blockchain.