Saul,
To be fair, referring to europeans as eurotrash is not confined to an anonymous forum, I'd quite happily use the term in person.
I've worked with several European militaries and found the Estonians and Poles to be very professional, but I've also witnessed others that add nothing beyond and increased supply chain burden. You are correct that not all EU members are NATO members, though the majority that aren't have a policy of neutrality, so I am not sure how that adds military value. Of those that do reside under the safety blanket of NATO peace and security, several are completely ineffective from a military perspective mainly due to size - please don't tell me Luxembourg, Malta, Belgium or Portugal are going to contribute anything particularly tangible in terms of defence.
Any EU Army will be dependant on the French, and as we have seen during Macron's tenure, that is a lever for national influence. I've always found the German's too guilt ridden, and scared to be seen as dominant, to provide any leadership on defence matters, and the French still seem to blame the anglosphere for liberating them when the resistance had it in hand. Since Iraq, the Europeans have become increasingly anti-US (even before Trump) and now are equally anti-UK (or certainly the EU is). As soon as the EU army club is up and running, the French will seek to put distance between Europe and NATO. It will go wrong, and the US and UK will be expected to pick up the pieces.
You may not share my view, and that's fine. I wish you well; you'll have some awesome parades, but don't expect anyone West of Brest to start blowing bugles in any hurry when you're knee deep in Russians and the French are shrugging their shoulders.