Actually, the US did kind of magic itself into existence due to a domestic labor and civil rights dispute. The states were primarily independent after the declaration of independence. It was not until Shay's Rebellion 10 years later that spooked the aristocrats into drawing our current constitution.

And to bypass your essentialized romantic patriotic history for a moment while utilizing your "common enemy" rhetoric, the EU has many common enemies and innumerable common and unique struggles. Consider immigration, the struggle for democracy, ecological responsibility, social justice, annexation by Russia. All issues individually more compelling than the rich coalescing their power to maintain control of the poor in a relatively isolated country with the population of Houston. The EU has so many good reasons to exist.