What have we learned from the EU experiment? That nations are real things. That national boundaries are not just arbitrary lines of division that frustrate the brotherhood of man, and provide excuses for war. The nation-state is a concept that developed along with the modern age, as Rome's cosmopolitan world order fell apart. And in a Europe that still wants the pluralism of a post-Reformation world, it still makes sense for people with a shared culture and language to stake out their territory and make decisions about the political, social and economic rules they're willing to live by.
The coal and steel cooperative may have been a good idea back in the day. Maybe it still is. But good fences still make good neighbors.