This is literally how cops trace cash

They mark the bills and hand them to criminal A, who they suspect works for criminal B. Then they wait for criminal B to deposit them at a bank, whereupon they arrest criminal B and use the marked bills (i.e. the trace) as evidence that he is part of the same mafia as criminal A

It's also very similar to how they arrest monero users: get some XMR to the criminal, wait for him to move it, trace the money to a KYC exchange, get his identity info, and arrest him

Lightning offers two huge fixes for this: you don't know what channel received the money (thanks to onion routing), and there's nothing to watch to see where it moves next (thanks to no blockchain)