It's a work in progress, Bitcoin can't be a Fiat alternative without fighting some war with centralised entities first and this can take years to accomplish and we shouldn't worry ourselves over it, my belief is bitcoin will make it happen anyways.
Well, not everyone would think like that since I believe both fiat and Bitcoin should exist at the same time. They can't eliminate fiat and switch to Bitcoin since only fiat is being controlled by the government therefore, they can have it. So it's just up to the people if they want fiat or Bitcoin, as long as there is a merchant who could accept Bitcoin or fiat if someone wants to withdraw.
So choosing between fiat and Bitcoin is still on a big debate.