Do you think it's possible Bitcoin will become a "global unit of account" in the future? If not, why? What would a world without Fiat really look like? Your input will be greatly appreciated. Thank you. 
1. For something like this to happen, I expect that we may need Bitcoin price fluctuate much less.
2. Don't forget that as long as the main currency of a country is fiat, the shop will have the prices primarily in the country's fiat and then converted to all other currencies.
So no, unfortunately I don't expect the prices be shown primarily in bitcoin. Not everywhere.
For all the countries give up their tools for inflation (i.e. stealing money) we need a powerful change. Maybe even a radical change in the way some people end up taking decisions for the countries.