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?
OP, I do not see this as realistic, bitcoin can be tracked down to anywhere it is being transacted. It is even more easier to trace when you transact direct from a personal wallet. Although it is a bit sketchy from exchanges because it all goes into one wallet and would need a well sophisticated device to do the tracing which is why you see that even hacked exchanges could easily trace their coin to seeing where it was transferred to and as well knowing the account or wallet holder who transacted with such wallets.
Irrespective of how bitcoin is moved around the chain, there are devices that could be used to trace transactions and i believe these are the device the government agencies uses to track bitcoin movement so as to apprehend wallets owners.