In my opinion, paper money will continue to survive because it has a physical, fast transactions with paper money or cash will continue to occur because human needs will be the same, namely buying and the needs of paper money will continue to be maintained, especially during the presence of the central bank.
Everyone who buys their necessities of life using paper money usually buys several kinds of goods for themselves at very affordable prices or in other words at very low prices. Why is that, because it is caused by the difficulty of carrying large amounts of banknotes or large amounts when you want to buy luxury items that are much more expensive.
That is one of the shortcomings that still exist in paper money so that the option for developing digital currency is clearly needed by everyone nowadays in order to make it easier to purchase transactions in larger sizes by only carrying one simple device. Yes, indeed paper money does not need to be eliminated from this earth as long as it can still be used and accepted by many people, but placing it in certain options is a very good thing in my opinion.
People can carry highest available banknotes, which makes it not so difficult to carry. For example this is how one million looks like:
That is not that much to carry. Fits perfectly in any backpack. But the think is - not in every country it is allowed to make so large cash payments. For example in some of European countries, it is not allowed to pay more than 7000 EUR for item or service in cash. You can pay 7000 EUR by cash and other part by transaction. Carrying isnt that much problem.
I can not support your idea of placing limits for cash. That does not make sense. You have earned it, but someone controls what you can do with your cash. I am for - let person decides himself what kind of payment is more convenient to him. I believe that very quickly people will come to decision that cash is inconvenient.