TG:-
Isn't the British Army an example why an EU army actually might work. I mean, there are Welsh, Scotts and even some lost Irish in the armed forces...
Well it might be, but perhaps not an ideal example. The British Army started out as various English Armies which over some hundreds of years dominated and defeated the armies of the nations that you mention.
That process has been part of European history as well of course, but every empire so formed has fallen in due course. That might be seen as more of a warning to the United Kingdom rather than a justification for a European Army...