I don't think that fiat will ever become worthless even price of bitcoin reaches to the moon as everyone is dependent on it for living and even if we have to use bitcoins we need to convert them to fiat first to spend them.
Specially true for countries that do not accept bitcoin as first preferred mode of payment. We have to convert first before transacting. Very cumbersome because we need an exchange for doing this and then pay the merchant. It better to pay in cash before wasting that time.
Yes right, some countries are there where government seek personal interest before anything else. So, they would never let something grow among their money that directly or indirectly reduce their income. Basically a world without taxes would be awesome, though its just possible when a decentralized currency like bitcoins takes over fiat.