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.
That's what I mean, you can't have countries with different political interest using the same monetary policy, an easy monetary policy will stimulate the hard working nation but crash the leisure seeking nation, but both a way of living and different view of life: In the long run we are all dead, some people will enjoy the life while others will work hard until they die
Normally, money has nothing to do, nor with economic results, nor with politics. Money is an asset that is used to exchange against goods and services and to store value. Whether things go good or bad, whether you have a lot of wealth or not much at all, shouldn't matter.
What is amazing with the Euro is that, since gold was not used any more in international economic relations, a state can go bankrupt without first screwing its own currency, as the Euro is not related to a state.
In fact, the Euro could even be used by non-European countries if they want to. Even if 3/4 of European states went bankrupt, that wouldn't - in principle - not even affect the Euro too much as a currency. Of course, the Euro would loose value, but not because states are in trouble, but rather because the economies are in trouble and hence what you can buy with Euros is reduced (reduced production).