Yes, sooner or later... But maybe not to crypto currency yet, maybe some other cashless methods. Have you ever seen people paying by cash in StarTrek, that's the answer to your subject question 
I think that it will be also extinct but its not the time now, because even now a lot of people are using cash. In poor country's people have no credit cards most of the time.
So they will continue use it as before. So we will need to help them in order to make cash extinct.