a myriad of other nationally orientated grudges being swept away
It's already happened.
The Eurocontrol UAC at Maastricht controls the upper airspace of the Benelux and NW Germany. Control staff from all the member nations working there, so you could be flying over the North Sea and talking to a Bulgarian.
In the interest of improved trafic flow it is quite common for control of portions of a national airspace to be delegated to another unit.
Of the original six member nations it was the British, the French and the Dutch who decided not to relinquis their sovereignity. Germany and Eire then renationalised the centres at Karlsruhe and Shannon respectively.
With current technology it is not important who is providing the service, only that it is all to the same standard, and that the systems be interlinked to allow a "seamless interface".