Who gets in the way of paper money?
I use them often and I have doubts that they will ever cease to exist. Bitcoin is not a competitor to them. This is a completely different system and it does not need to be compared with fiat.
I do not think that the question is clear enough in the OP because there is paper money that is fiat and paper money that is not. There has not been one fiat system to last but water and food have always been currencies. I think that the global economy is too large for paper money to not exist,