For the relevant of what Bitcoin stand for which is it's decentralized nature and knowing what this stands for means the government will always hold on to what they can have full control of which is the fiat system hence Bitcoin can never come to this spotlight in other to protect it's relevance as a financial freedom and there is no system that can function without the existence of government, Bitcoin was never created to replace the fiat system and of course that wasn't the reason for it's invention but to work in hand with the fiat system and I don't ever imagine Bitcoin replacing any of the traditional money.
Yes the fiat currency would continue to exist except maybe in future, different government decided to embrace Bitcoin as their legal currency but I doubt if it would be possible cause of how volatile it is and won't be suitable for carrying out transactions by market sellers and business owners anyways Bitcoin was to serve as an alternative to fiat against third party but currently it's more like a store of value and people would rather hold it for years to be more valuable than use it for carrying out daily transactions like the fiat currency.