That peace in Europe didn't start because of the EU, it started because western Europe was conquered by the US and eastern Europe by USSR so they were a bit too incapacitated to fight each other under those conditions and given the much bigger issues they had at the time.
Yes, and the European Coal & Steel community didn't stop the slaughter, the nuclear powered US stopped did. The stopped slaughtering wouldn't have continued without the EU. Everyone in Europa couldn't have kept doing it even if they wanted to with 80 US military based on the continent.
You give the EU too much credit for peace. In fact, there's way more tensions between EU countries now as EU members than in the past. Poland even went to buy weapons from Korea and build them on-shore because they don't trust buying weapons from France and Germany. Just because EU countries aren't slaughtering each other, doesn't mean they like or trust each other.
You can say what you want, but take any history book and you will see that what we got now is the longest period in history without a war between European countries. They don't fully trust each other? OK, but this is still a great improvement over the past.
That peace in Europe didn't start because of the EU, it started because western Europe was conquered by the US and eastern Europe by USSR so they were a bit too incapacitated to fight each other under those conditions and given the much bigger issues they had at the time.