> So... is there some way to have both the benefits of multiple currencies and a single one?

Look at the USA as an example. The difference with the EU is that the USA are vastly more homogeneous and I believe there is very little opposition to redistribute wealth from richer to poorer states. The EU is fragmented, almost nobody wants a tight political and fiscal integration. What would be of the USA if state governors were much more powerful than the federal president, to the point that few people would know who the president is and what he can do? This is the state of the EU.