Fiat currencies definitely aren't necessary, there is an increasing trend towards digitization of currency, and blockchain based currencies are just the next generation of this. The problem is that Bitcoin came out, and everybody treated it as the successor to fiat currency, rather than an incremental improvement on digital currencies such as Paypal and Skrill. I think that if Bitcoin was never invented, but somebody like Paypal had implemented a blockchain technology first, then we wouldn't be in the rivalry scenario that we're in now.
Fiat currencies obviously is necessary even though digital currency now is becoming trend that keep increasing and improving. The existence of digital currency and crypto will never replace fiat currency because in some context it is becoming the proper and effective means payments. Do we can't replace fiat by digital money? I don't think so. However, fiat and digital money as crypto currency should run together.