Why haven’t electronic payment systems completely replaced paper cash and coins?

In addition to some great answers given, you might also wan to consider the following:

• Grey (or Parallel) Economies, mostly operate via Cash. Grey economies are those that are not documented. Transactions in the grey economy are mostly cash related so as to avoid tax and/or not been seen as a transaction that is taxable.
• Black economy, which for obvious reasons prefers cash to deal with and then launders that money through the system
• Underage use of money. A 8 year old can take a $ 1 note and buy toffees, we cannot expect 8 year olds to be using digital systems for payments
• Access to technology. Even in developed countries their are people who simply do not have access to digital technology. They have issues with basic necessities like clothing, shelter, food/water.