It seems impossible to realize such a thing. Because the policy of each country is different, its needs are also different among fiat. If something like that happens, the economy of each country will be destroyed. You can imagine each state price of a material 1 with another different while the same nominal value, then there will be losses and resulted in the country looking for alternatives to create their own value of a goods / produce a good. So long over time the value of the currency is abandoned. If making all nations seems impossible because there are significant price differences between countries. As well as the above illustrations.
Of course the price will vary. For example an apple in the US would cost just $.50 but if it will be shipped in other country let say in Asia it would already cost $1. But it would be nice I think. There is no need for cash exchangers and it means no transaction fees either. I actually love the idea of having one currency in the entire world.