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.
Paper money will cease to exist. First, their production costs money, the second counterfeiting brings damage to the economy, in the third government does not control, and current trends lead to gain control over people. Be it bitcoin or the national currency is not important.