That was my point. They do.

Nothing is tracking the serial in a person to person transaction. Put it in a bank's digital currency system and it gets traced. Take it out, no longer traced.

So all they see are exit and entry people points. 

 I like cash, but keeping it in circulation without touching an ATM is not always easy. If not yourself, your counterparty will log the serial number at your bank’s local branch. 

 You could always burn off serial with a laser...