> Do you believe that if the UK leaves the EU, France and Germany will go to war? If not, I don't see how "created to prevent another world war" is relevant.

Directly? No. Trade war between EU and Britain? Might happen.

And if the EU doesn't take fairly drastic action to, it will fray further, essentially destabilizing Europe. No war will come from that, either. Not yet. But if the EU were to crumble, it's a good bet there'll be a division between haves and have-nots. We're still not at war - but the have-nots have crumbling economies now, creating unrest. Meanwhile, the few haves that are left over are likely to envy each other what little they still gain from such a union. Sooner or later, we'll go back to individual states. A few strong European powers, not bound by the EU any more, and many crumbling economies around it.

Meanwhile, the pressure on the smaller states from migrants and refugees increases. (If you think we're done with middle East and African troubles, I suggest you take a look at climate projections). They will start to let them pass through and/or ignore them, because they have to, to survive at all. There's not much political clout left to move the agenda on a global scale any more, so that option is out.

As a result, the stronger countries militarize their borders. Sooner or later, somebody will mount a preemptive mission into some of the smaller countries, simply because it "makes sense" to stop the flood of migrants earlier.

Play the scenario from there.

Sure, nothing guarantees it will happen that way, but there's a good chance something like that will happen. The point of the EU was to prevent that - to make the common bond so valuable that nobody would want to risk it.

Britain's voting public decided that the value was low enough. If the EU wants to have any relevance in the long run, they will need to make it clear to Britain that yes, that bond is pretty valuable, and tough luck for Britain.

That is how it's relevant - in the very long term, as a stabilizing force.

And no, it's not "Don't leave me or I'll hurt you". It's "we had a contract, you broke it, that means I don't need to uphold my end of it either". That's generally how this whole treaty business works.