I guess it would be nice if that happens. Transactions will become easier and more faster. But in reality fiat still rules the market for a very long time.
To be honest I do not think fiat money would be fully disappear and our county wouldnt be a cashless society since its been part of our live for so many years. But I think bitcoin would be one of the leading currency sooner or later.
Even there will be more currency being develop and bitcoin leads the way to make all transaction easier, it can be impossible to vanish fiat because it is controlled by the government. It is nice to have something to be use in online transaction with anonymity, more fast and convenient but cannot use for everyday payment because the price is very volatile.