Governments are instituted...
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,...
.......................Thomas Jefferson, Declaration of Independence
A worthy ideal, indeed, but more ideal than reality in general. Mostly, I think, governments are instituted to protect groups of people from rival groups of people. People have lived in competing groups since time immemorial, and before people, the same was likely true of their prehuman ancestors, as it is true of our closest animal relatives. With luck, your nation protects you from your fellow citzens as well as from external marauders.
The combination of memory of the horrors of WWII and the threat of the Communist East persuaded much of Western Europe to form the European Union. New economic and political tensions, combined with the considerably diminished threat of Russia are now threatening to tear it apart. Some of the problem was doubtless due the too rapid expansion into a mostly unprepared East - let's give the Idiot President his share of the blame for that.
Fundamentally, though, the problem is that the centrifugal forces are tending to exceed the centripetal. The multi-cultural character is a problem, but their is no strong central government. Without it, common fiscal and economic policies can't truly exist.
The United States, under the Articles of Confederation, before they were the United States, faced a similar problem. Thanks in part to those Barbary Pirates we got a constitution and have managed so far to preserve it. I would guess that the odds are heavily against the EU achieving similar unity, and I suspect that the current union is a metastable state, quite likely to spontaneously decay.