More crucially, neither is preventing warfare. After WWII, the victors believed that another large war could destroy humanity - not necessarily because of nuclear weapons, but due to the incredible damage their WWII technology did, and considering future improvements. The UN and (the predecessor of) the EU were founded especially to prevent another major war.

Also, they knew, after WWI and WWII (and all the prior wars) that without serious effort and dedication, warfare can happen whether or not anyone really wants it.