This assumes that the operators of the tumblers are to be trusted and aren’t state actors themselves. It would be a pretty smart move for the Feds to run one or more of those operations.
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.
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.
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.