You're right about the integration, but the very point of EU from the beginning was an alliance of fundamentally different Member States pivoting around the LOWEST COMMON DENOMINATOR OF SHARED VALUES. What we got in EU today - including the time-consuming consensus-based decisive process is the best thing we can have without going back to the dark ages of 19th century in-fighting. EU is a very complex beast, but in general it DOES work well on the topics that involve complex negotiations across 27 countries with conflicting interests, which led huge economic growth for both the new joiners and sustained economies of the old members, a classic win-win.
There's an excellent book from an insider about how EU operates in reality, that skips all the 'straightening cucumbers' nonsense invented by British tabloids:
https://www.amazon.co.uk/Enraged-Citizens-European-Democratic-Deficits/dp/0857423622