In order to implement mass surveillance with dollar serial numbers, you would have to identify people during transactions and record them. Nobody taking cash does this outside of ATMs possibly. When I go to the store they don't ask for my ID to pay with cash, they don't record serial numbers, it would be a lot of technology and effort and there's no justification for why. When doing transactions with computers, there's usually a reason for attaching an identity to a transaction, a reason for keeping track of things, addresses, account information, login details, etc above and beyond just banks being required to keep this information.