I personally don't think that bitcoin will defeat FIAT . at least not for the next couple of years.
It's all about what it came "first" . just an example "Bitcoin" is the first cryptoo currency => the most used. and not the other Altcoins it's the same on this case for Fiat money , Fiat money exist for thousands of years.
Fiat hasn't existed for thousands of years. Your confusing fiat with money. Money has been around for a long time, almost always in the form of Gold. Currency backed by Gold isn't fiat. Plus history shows true fiats have a shelf life. Can fiats exist in a continous boom and bust cycle? Sure. But with Digital currencies on the horizon it's a bit like choosing to heat your house with oil lamps than electricity.