Fiat currencies, like the Euro and national currencies, are just such a simplification that leads to a non-optimal solution. We see that non-optimality starkly in Greece (and Puerto Rico, and Detroit) where a semi-independent government body gets into financial trouble, and the resulting exodus of the best people from that area exacerbates the disaster.
We don't need fiat currencies any more. We can handle the complexity of multiple proof-of-work currencies. You go to a shop that wants payment in gold. You point your phone at the displayed price and it will display the conversion in currencies you have. Online purchases are even easier. Of course we are assuming a mutually trusted body to hold and track the ownership of that physical gold. This can be augmented with cryptographic currencies (like bitcoin) and by cryptographic proof of transfer of centrally held physical stuff (like gold) held by one or more trusted parties.
For small payments fiat currencies will continue to be important, and we can presume that people selling small amounts of stuff will continue to be required to accept them.
One of the advantages of fiat currencies is that they enable the government to raise money easily in an emergency (such as a war) by simply printing it. This is a tax on people who happen to hold the currency or who are owed money denominated in the currency. This will likely continue to work for small items, while for large items IOUs denominated in various currencies can be required to be accepted in a proclaimed emergency.
There is a really big advantage of moving to a proof-of-work currency that is backed by physical stuff held by multiple trusted central services: The physical stuff doesn't have to be useless (like gold or bitcoin). Instead it can be non-perishable stuff that might be useful at some future time. It might, in other words, double as actual preparation for some difficult future circumstances.