I think completely the opposite is true: paper money has no trail whatsoever. You can cart it accross borders and no one has a clue. It's far harder to do that with online money, as although it can be done, removing how it was done is far harder.

Most money doesn't exist. Banks only need a percentage of their funds in monies to be considered solvent. They lend far more out than people invest in themselves. Then there's stocks and shares - more money that has only theoretical existence. Google lost $13bn, but no money as such changed hands. And the future exchange is even more ephemeral: plcements of money you don't own in items that don't yet exist...

Yup, money is pretty sidelined as a real item.