Earlier quoted context omitted.
This isn't so far fetched. Cash registers already have Internet connections and can be outfitted with cameras to record all bills going in, except maybe those inserted in a stack. And ATMs might already be recording serial numbers of dispensed bills. Essentially they might/could do with currency what they do with license plates, which is track where everything goes and at what times.
Like 0 cash registers I have ever seen employ this.
If the banks track serial numbers, they could probably build a fairly complete picture of what kind of transactions are going on. With the vast amount of data, you could probably fill in a lot of the gaps.