The last part is the important part I think:
"" Organisations such as the EU and UN have bound Germany in close ties with other countries.
"""
Looking at the roots of the Coal and Steel Union, it was a desire to prevent any more wars in Europe. The strategy was to tie France and Germany into a world of cooperation where it would not make sense at all to have any more conflicts.
Whether the additions of countries into EU will make it too big and too un-manageable is a good question. Also insofar as the new countries have other values and more structural problems.
That points to another 'fact' = Countries at the same level (more or less) have a chance. Too disparate and it will fail.
Did it then require the total devastation of Europe to see the light? maybe.
So, if it is not free trade which will be the issue but rather the political, economical, social and military cooperation governing 'peace', then a proto-EU could prevent another war.
Western Europe has been at peace and it is not likely that another war will break out in that part of the world. Eastern Europe - as in Russia, etc, is another thing all together.
IF France, Germany, Italy and Spain had come together in the early 1930's to form a power-bloc, I believe things could have been different.
BUT: That would have required a totally different set of leaders!
Ivan