I get all my ideas from this book, so my view on this whole thing may be limited.
The EU is not built to unify the nations that compose it to have a single voice to the outside world; it was built as a tool to elevate the nations' democracy so that they wouldn't fight between each other. It is a club with cool privileges, but if you want to get in you have to work on yourself to be better. It is a club turned towards its members rather than towards the outside. The endgame of the model is not to have a unified Europe that can talk with a single voice to the rest of the world, it is to integrate all countries of the world into the same model; in order to do that, other countries will have to make some changes, improve the quality of their democracy, respect the rule of law if they want to have a chance to enter the Union. Not everyone can enter (it wouldn't make sense if everyone was part of it), but everyone can improve and be part of a regional equivalent.
We already see that kind of thing happening with different regional convergences such as ASEAN or UNASUR. None of the country has the intention to merge with another, but they still want to be heard on the world stage and they have to improve their way of working to do that. The EU is just another bait and switch system, but the consequence is actually excellent for the nation !