I don't agree with that. We had two powers dividing Europe in two, placing their own armies all over the place and doinglg their best to convince the other party that the world would be destroyed if it dared to attack. That was what brought us peace. Collaboration in the form of the various European international organizations was a consequence.

Making another war in Europe was basically impossible. We had one in Yugoslavia which was not aligned with the two blocks and anyway only after the USSR lost the cold war.

The idea is that EU countries do not see themselves at rivals, this is very different then our entire history where everyone had an issue with their neighbors (there are exceptions of neighbors not having any conflicts). Most educated Europeans are now considering the entire EU as a similar culture and not want to start a fight to kill each other for some historical land, the exception are the uneducated or just low IQ people that fall for extreme nationalists that push for "Make our country a great empire again"

Your point is about the Cold War, nuclear weapons prevented nuclear alliances to attack each other, it did not prevent say two NATO non nuclear members to start conflicts.