What OP suggested is similar to Euro, a single currency across boarder, and you see how much trouble it has now

In fact, the Euro, as a currency, is behaving amazingly well. Those in trouble are STATES, not the money itself. States who gave up their fiat currency to become *normal* economic agents under a currency they don't master themselves makes them go bankrupt, because they were used to reap in all the cheating that happens with a state fiat currency (essentially reaping in all the seigniorage of counterfeiting). The most corrupt states (the south) suffer of course more than the less corrupt states of the north.
The biggest danger for the Euro is, as usual, political mixing in the monetary policy, which, according to its statute, shouldn't happen.
The Euro is not on the verge of collapsing. Some European states are. That's different all together, exactly because the Euro is not a state fiat money, but an inter-state fiat money.
Several states didn't realize the amount of power they gave out of hands when creating the Euro. I'm personally happy for that, but I think some regret it.
The Euro doesn't have the status of the US dollar yet, in the sense that I don't know of any foreign country where Euro's are actually used as actual means of payment instead of the local fiat currency. And the weak economic situation of the Euro zone at this moment is not bright either, but that has nothing to do itself with the currency itself.
The uncoupling of monetary issues from economic policy and policy in general is the best thing that could happen and I only know of the Euro in recent times that did such a thing. The Euro is not as good as gold, but its principles are more sound than that of a state fiat currency that is much more exposed to political manipulation.
Nobody would blame gold to be the culprit of a state going bankrupt (as was almost the case with France under Louis XV after inherting the state from super spender Louis XIV). In the same way, the Euro is not to be blamed for countries like Greece to go essentially bankrupt. They were simply not used in keeping the books in order.