The fall-out of WWI was the break-up of three tottering empires and the creation of numerous nation-states in their place.
A generation later, Hitler wanted to unify Europe and was very nearly successful until was defeated.
Is it because this is the elites kind of unification that it's considered desirable?
The kind of "elite" we're talking about here, are people who are proficient in intrigue and manipulation. They are much more interested in a single EU bureaucracy running everything, because that would give them more room to work behind the scenes.
The elites miss the old kings, where the path to wealth and power involved the ability to flatter the king, and charge vast sums of money for access to the king and for the ability to influence the king. Having to satisfy customers, meet payrolls, and figure out how to deliver high-quality products seems, well, common and distasteful to these "aristocrats of pull".