These are strange monetary times, with negative interest rates and central bankers deemed to be masters of the universe. So maybe we shouldn’t be surprised that politicians and central bankers are now waging a war on cash. That’s right, policy makers in Europe and the U.S. want to make it harder for the hoi polloi to hold actual currency.

Mario Draghi fired the latest salvo on Monday when he said the European Central Bank would like to ban €500 notes. A day later Harvard economist and Democratic Party favorite Larry Summers...