There may be some short-term pain for the UK from this, and God knows they have their own problems, but the EU is a sclerotic and failing institution even apart from the challenges posed by Brexit.
There will likely be something that calls itself the EU in 30 years--God knows these institutions have a way of lingering--but it will be a fractured and largely irrelevant body, if current trends continue.
And I don't see how the EU has any chance of weathering the next economic downturn or handling its serious demographic problems, let alone coordinating a serious response to any kind of security threat. The mettle of institutions is tested by bad times, not good, and the EU has yet to successfully surmount a single major challenge; all it has managed to do is kick the can down the road on a few issues.
As far as the claim that the EU is the cause of Europe's peace post-WWII (only true if you don't consider the Balkans part of Europe, but never mind). My current thesis is that while there is a correlation between peace in Europe and the creation of the EU, the causal relationship is largely backwards from how it is normally understood. The EU exists because American military hegemony largely short-circuited the need for intra-European strategic considerations in Western Europe (obviously the conflict with the Warsaw Pact was another issue). Various European countries were able to leverage this peace to advance their economic interests, which they could only do because they didn't have to worry about their neighbours, for the first time in recent history.
The fact is that if American continues to withdraw as its interest in hegemony and maintenance of the global order declines, intra-European strategic competition will increase. That alone will tear the EU apart.
