If you're e.g. a retailer, you can maybe know your coins are clean one step out, but you can't know if they're clean for their whole traceable history without standing up a fancy Network Analysis OLAP cluster and hitting it with some really high-cost queries.

Let me put it this way: what would you do with your float if you run a convenience store in a bad part of town, and know that there are marked bills floating around in the local economy, and that the police might pop in at random one day and take them out of your till? Well, you'd probably deposit your float in your local bank at the end of each day, and then get new, guaranteed-unmarked bills from the bank. That's mixing! It's not money laundering, just mixing. You're removing the potential liability of being blamed for what your customers' employers' customers' employers did.