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 only redone the likely chance of tracing the coin back to the owner. The best that can be done is to use a mixer, coinJoin or to convert to a privacy coin like monero and convert back to bitcoin. But sending bitcoin though many hops before getting to the target addresses is also a good option if the transaction is done at different time like days between, using many addresses and also better if you divide the coins into different addresses in the process.