I don't think Bitcoin can be anonymous if it goes through an exchange, because you have to create an account with identifying information. I you host the endpoint yourself, it may be possible to completely mask the source, but I'm really not sure.
But it may be moot if the exchanges simply mark any bitcoin that has gone through a tumbler as tainted and refuse to convert it into anything else.
Imagine a money laundering operation, where every laundered physical dollar gets a physical stamp of 'THIS CAME THROUGH A MONEY LAUNDERING OPERATION'. That's the current state of BitCoin tumblers.
Assuming they can actually identify it as having gone through a tumbler, sure, but it's not like tumblers advertise the addresses they use. Especially not distributed systems like CoinJoin. These are just ordinary transactions that happen to include inputs and outputs from multiple, unrelated sources. Following long-established best practices, any given address will only be used once.
They could ban exchanges from accepting coins that do not come directly from another authorized, compliant exchange, but that would be tantamount to banning cryptocurrencies altogether. It wouldn't stop them of course, just drive them underground.
edit: To expand it's harder than tracking normal money laundering too because the "businesses" (ie wallets) can be generated by the thousands per second.
No, they're not in the source code itself, but without them the project would still be sputtering along in almost total obscurity, if not abandoned altogether by now.