If everyone starts using electronic money, infrastructure will also need to be developed proportionately. It will not take too much time for paper money to disappear from the market. At the present time, it is not yet clear whether financial institutions can adapt to that change in a timely manner.
I reply again but in my opinion your point is not clear. You mention electronic money (what do you mean? Crypto?). You seem to make a big confusion with cash disappearing leading to more use of Bitcoin/Ether etc.. but there is no connexion between the two. A country could very well make cash totally disappear, and in the same time also ban all crypto-currencies.