You can argue all you want that a European Union was a good idea. Maybe it was. However, the EU was poorly thought out. If they wanted a union that would have worked better, they would have formed a republic. As it was, the EU was just a half-azzed attempt.
One of the founding ideas behind the EU's formation was to reduce the likelihood of another European war (e.g., Germany attacking its neighbors as it did on three occasions within 70 years - 1870, 1914, 1939. To this end it has succeeded by intertwining economies.
Actually a republic was proposed and quickly discarded as no one was willing to relinquish sovereignty. Here is a summary of how the EU is governed - see:
https://www.fas.org/sgp/crs/row/RS21372.pdf
