The end of paper money will happen for sure. Most of us already use debit cards for most purchases.
But there is a bigger shift on the way, with central banks issuing national cryptos side by side with fiat, which will likely phase out fiat eventually. There are plenty of examples of this type of thing historically as monetary instruments become obsolete or transform with technology.
The article below has more info on all this. The 'Banker's Bank' (BIS) in Switzerland is already seeing this trend with central bankers.