Older mixers you could argue could kind of be traced but even then there’d still be difficulty and deniability.

There’s a newer class of privacy mixer though that basically is untraceable. On privacy chains you can’t see the transactions so from an outside perspective it looks like the money just went into a black hole and it wouldn’t show up until it got converted to public again. When it gets converted to public though, it has no connection to the original transaction and could be literally anyone else’s money who used the chain converting to public.

It could take a long time but you could basically just slowly do this and withdraw small enough amounts of money to not raise suspicion. Or do something like start your own coin and pump the price with the stolen funds then cash out the coin. There’s new privacy smart contract chains where this could be done without even signing slightly the stolen funds were used.

It’s kind of a mess.

That's exactly what I thought as well, especially if the transaction is done electronically, it should be traced back to the person who made unlike with cash.

Yes, but only if the organization is cooperative. Say you are a cop in Paris investigating some shady bitcoin transactions. But the mixer is in Japan. So you spend a year getting their records, only to point to another mixer in Canada. The goal isn't mathematical untraceability, just increasing the burden on investigators to the point they move on to easier targets. There are always lots of speeding tickets that need handing out.