Ken Rogoff offers a series of powerful arguments in favor of retaining paper currency. (Of course the feasible alternative, for Rogoff, is not commodity money, but 100% fiat electronic currency.) In particular, the widespread use of paper currency (1) makes it hard for central banks to push interest rates below zero (they would have to rely on some weird scheme for taxing currency, a la Silvio Gesell), and (2) allows people to conduct transactions securely and privately, without monitoring and expropriation by the state.
However, as Rogoff points out, there are important drawbacks of retaining paper currency. (3) The anonymity of paper money makes it popular, and strong demand for money gives the central bank plenty of opportunity to expropriate wealth through seigniorage. Moreover, (4) if a government were to eliminate its own paper currency, people might start using other forms of non-traceable money (Rogoff mentions paper currency issued by foreign central banks, but private commodity or even private fiat currency is another, far more attractive, alternative). As long as people are reasonably satisfied with the government’s currency, they are less likely to develop alternatives. Replacing government-issued fiat paper money with government-issued fiat electronic money might help push people toward superior, private solutions.
Oh, wait, I got that backwards. Rogoff mentions (1) and (2) as costs of keeping paper currency, (3) and (4) as benefits. If you reverse the signs, his analysis is quite insightful.