If crypto replaced fiat, markets would become centralized. A decentralized market where crypto and fiat exist simultaneously would be preferable and provide greater options, value and efficiency to the public. Fiat has its place. An exchange of paper money is more efficient and convenient than an electronic transaction. Buying/selling without point of sale devices, cellphones & accessories being obligatory is an important paradigm to ensure the right to buy/sell never reaches a point where it becomes unattainable to those living in poverty.
There are blurring lines between crypto and fiat. Ethereum with its undetermined supply of coins is little different from fiat which can be printed according to whatever subjective and arbitrary mood swings seem like a good idea over the short term.
Core principles upon which bitcoin was founded shouldn't be cast aside nor abandoned for the empty promise of "a few bucks more". This is where algorithmic supply has a huge advantage over arbitrary and subjective money printing. It ensures stability which leads to long term value.
I think it would not totally eradicate fiat money because their will be a need for some accumulated wealth by anyone. And they would need to make another blockchain for btc because if ever most of the countries will use it as transaction, there might be another issue and there facility would have to be more larger than before to confirm all transaction thats coming all over the world.