Economic outlook:
May not be the end of the world as we know it, but the empirical rule of thumb for big splits isn't good. Some examples, which could proxy a big economy dropping from the EU:
1) American Civil War -> Confederate States in the Union
2) Soviet Union -> Russia and the Commonwealth of Independent States
3) Korean War -> North vs South
4) British Empire -> Britain and the Commonwealth
Rough trend: the economic activity lost in the split, and the years onwards, could easily fund another state GDP-wise equal to one of the biggest economies departing; former glories don't return; recovery period is longer than people would like to imagine; greater freedom and more citizen-power is far from guaranteed and can regress; the biggest (absolute or market terms) of the parties in the split benefits the most; middle classes take a dive, the poor are decimated; hasty post-split deals are messy, cost a bomb and are still a bad compromise!
Political bonus:
League of Nations -> ECSC, EEC, EU, UN
Dictats and good intentions of powerful independent states aren't good enough to achieve global goals of peace, prosperity and the rule of law. As soon as the dynamic between powers changes, the shocks cause too much material, economic and cultural damage -- nobody's free when war comes knocking, or you can't pay your bills. This compound damage, like economic crises in their own right, must therefore be minimised -- no-one wins otherwise.
Thus international organisations need both regulations and the means to enforce them to be effective. The international political, security and market bodies, which emerged as a result of previous debacles, learned this lesson the hard way from the shortcomings and failures of the LoN.
The most important conclusion being: politics is not a zero-sum game, particularly international politics. Hence we get the democratic idea of the free common market blocs tied by democratic institutions, state-capitalism and necromancy (trying to resurrect or cling on to the specious ideas from previous eras). Europe went with the first option.
There's a libertarian counterargument to this development, but broadly it has several problems too: a) lack of perfect information for decision making b) Platonic conception of rationalism, from which rational free states and individuals spring (reason and intuition are superior to experience, and the chief source of truth) isn't sufficient to describe and manage human affairs c) free states and inviduals aren't 'naturally' good when left to their own devices d) the arbitrary ruler dilemma (strong personalities and states dominate, how do you ensure a fair exchange?) e) by approaching uncertain total freedom, you somehow 'absolutely certainly' converge on the common good f) moral values are 'natural' they do not require explicitly stating or maintaining g) the market is a 'natural' and amoral system of free agents acting in their self-interest, which always results in the accurate picture of said system; where assuming peoples' positions and anticipating prices, from the point of optimal strategies and information, is therefore as valid as physical law and can be relied upon to deliver the best result for everyone (even academicians don't avidly cling on to this any more).
In general libertarians claim quite a reasoned argument, but eventually end up with appeals to natural law. Debates can be had here. But they haven't yet produced a solid 'state-lite' model yet. General principles are only good in as far as they produce specific policies, when you come down to it. What limited libertarian nuggets have been tried in the context of neo-liberalism , they haven't quite delivered on the promises.