Complicating the question is the recognition that even today's greenbacks are not completely anonymous. Paper money has traceable serial numbers. In the near future, cash registers could automatically scan and record those serial numbers while unobtrusively snapping a photograph of your face. In the slightly more distant future, it might be simple to do a DNA analysis of the bills to see who's been handling them. In either case, a network of merchants, corporations, and government agencies sharing this information could trace the movement of your cash through the economy.
Computers are extremely flexible.
It's a well-known axiom that they do only what their programmers tell them to do. In the digital sphere, anonymity adds complexity. Digital cash programs and protocols need to be much more complicated than today's credit card processing systems, for example, to provide the anonymous, unforgeable, and untraceable characteristics we expect from cash. People want it. But corporations and governments don't.