If you ask me, IF BTC becomes the dominant world currency, fiat would still be around BUT it would slowly base its value on BTC, rather than BTC basing its value on fiat.
That is if btc will be successful in dominating against other world currency but why do you even think of it dominating atm if Bitcoin itself has gone astray? Instead of it being used as a currency, it is seen by most of it's users as an asset. I can say this for certain because most of us here hodling bitcoin just speculates how it's price will be higher tomorrow and how we will get profit from it. That's not the proper use of a currency IMO and for btc to dominate world currency, it needs to be used in transactions more.
Yes thats why I typed it as a BIG IF. Read kesany's post to get the context.
On the topic of BTC not being used as a currency, I have already made that argument a lot of times in the Market subforum. No one is willing to use BTC as a currency because fiat and credit cards are more convenient and more accessible for everyone. BTC is more useful for darknet purchases and maybe other illegal or under the table transactions.
Having that said. Why would I waste BTC on regular items when I can use fiat?