It's basically like a giant, real-life version of the prisoner's dilemma.
If all countries decide to put their own interests aside and concentrate on the greater good, then everybody wins.
However if everybody decides to put their own interests to one side, apart from one country (which for the sake of argument we'll call "France") which decides to be a selfish asshole, then the selfish asshole country wins.
Seeing as we know that France is going to act like a selfish asshole, there is no logical reason for us to be self-sacrificing.
Yet it's not just a PD, it's an iterative PD because it's ongoing through time. Such problems
have been solved, through reciprocity. There's an interesting book on these very problems by Axelrod, that explains that punishing non-cooperators once (immediately after previous defections) in iterative PDs and cooperating if they cooperate leads to the greatest cooperation overall. People instinctively know this, and world leaders certainly do (with few exceptions, like the near-permanent embargo on Cuba).
In other words, throwing our hands in the air and going "it's a prisoner's dilemma - we can't do anything!" doesn't mean that the problem is insoluble. We can and must cooperate with Europe, and they know that too.
Your logic is completely self-defeating, because it applies equally to the development of societies - clearly it didn't stop people though. Assuming that the member states of the EU are out to screw each other over at the expense of others
is exactly what the EU is designed to stop, and is exactly what I meant when I said that you were missing the point of the EU. Every leader knows that, in cooperation, the result is greater than the sum of its parts: it's not rational at all to defect from that, because of the possibility of reciprocated punishment in the future, which will happen for the express purpose of ensuring mutual cooperation and therefore mutual prosperity.
There is a lot more than just population size to consider.
Like the economy, which it was I was referring to.