I'm with you on this one, but with nuances.
The roots of the EU were in 1950-1952, with Schuman's speech and the ECSC creation. The main purpose, right from the origin, was the 'Never that again' motto (and it still is, for the reasons you pointed out). It was not really the good times then, not yet.
As you say, Europe is a continent, not a country. But we have a common history, and possibly a common destiny. Saying that we have no common culture is a bit overstated. Our differences show better than what we have in common, but, at least in Western Europe, I think we have quite a bit.
The mistake was to try and marry so many people in such a short timeframe. Instead of making Europe stronger, our politicians made it larger, and obviously weaker. And when Europeans disagreed (referendum in France and Ireland), they just washed their hands. F**k the vox populi..
This is a marriage of convenience, very true, but sometimes convenience last more than love.
Hopefully it does,
Barnab?