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.
You say that Fiat money is not needed, but you are not quite right, any Fiat currency is supported by either useful resources or the in gold, and the cryptocurrency is supported by Fiat money. There will always be Fiat money and they are very necessary for both the person and the economy, so do not jump to conclusions, we use Fiat money every day and this system will not go anywhere.