Fiat will be replaced by another currency, not sure that is Bitcoin or Cryptocurrency, I think no government will allow Bitcoin or any other created Cryptocurrency by the people which is uncontrollable, every government have a tendency to dominate and control over any currency, Every government has an agency which is Central Bank, So without approving by themselves, Bitcoin and Cryptocurrency will be in the mainstream ever, So I don't think that Bitcoin or any cryptocurrency will not replace of the Conventional Fiat very soon.
Fiat won't be replaced
The fact of the matter is that the average joe trusts fiat and all the institutions around it more than bitcoin. Because bitcoin is still immature and the eco-system around it is not yet robust. Think how often you hear of an exchange being hacked and people losing their money. And then think of when you last heard this happen to a bank. Till bitcoin solves the vulnerability of the interfaces like exchanges, there will be no adoption.
Bitcoin cannot "solve exchanges", exchanges are beyond Bitcoin. It is not Bitcoin's business what people are willing to exchange it with.
If you earn Bitcoin, and spend Bitcoin, you are not using exchanges. That is what Bitcoin covers, its own network and only that.
As for fiat being replaced, give it a century or so. I predict by then the crypto algorithm would have been replaced by a quantum one, but other than that, it will probably be used.
Governments can do whatever, that won't stop Bitcoin. My government forbade forex for nearly two decades, before finally giving up. A Central Bank is useless in a post Chicago, Austrian economy where banks don't do fractional reserve anymore. Deflationary money doesn't need banks in the first place. Bitcoin doesn't lose its value over time like fiat does, therefore you don't need a bank to gain interest (which is always lower than inflation anyway).
There is also the generational transition, the older people opposed to Bitcoin will go, and the younger ones more willing to accept it, replace them in seats of power. The genie is outside of the bottle the mere Bitcoin idea and its working implementation serve to prove it.
Yes, time is in favor of Bitcoin. Out with the past, in with the future. Its already accepted worldwide today, underground in some places, openly in others. It can only improve from now. Thankfully the opposition is authoritarian and few, and old, they cannot escape time.