That's what some people would like the EU to be about. Fortunately, there is a healthy diversity in people's views on that issue just as with many other issues. Thus, in practice, we have always had European integration on several different levels depending on the individual needs of the nations involved and their collective benefit from co-operation.

Today, being in the EU is not the same as using the Euro. Though the Lisbon Treaty blurred a lot of lines, we historically had the European Courts of Justice rather separate from the European Union as well. There is a lot more historical detail on Wikipedia's page on the EU if you're interested.

If anyone thinks Europe will still look the same in five years, I think they are probably missing something, given the obvious differences in financial power between say Germany and Greece today and the obvious negative effects it is having on the better off nations. Who knows the consequences at this stage? Maybe the result will be closer integration where the financial policies of the weaker nations are restricted by the stronger nations who support them. Maybe Europe will fracture as an economic community but perhaps continue as a legal, diplomatic, free trade, and/or military one. It is clear that on matters like the privacy issue at hand, there is a lot of common ground on the basic principles regardless of economics, so I suspect that side of things will be maintained.