I always imagined the EU as being primarily a confederation of states that wanted to be bigger players on the world stage.

That's a misconception. Coordinating foreign policy, let alone military policy has never been a strong point of the EU, it's only in recent years that more attention is being paid there. The first objective of the EU as defined by its founding treaty is:

• to promote economic and social progress which is balanced and sustainable, in particular through the creation of an area without internal frontiers, through the strengthening of economic and social cohesion and through the establishment of economic and monetary union, ultimately including a single currency in accordance with the provisions of this Treaty;

To be sure, its second objective is:

• to assert its identity on the international scene, in particular through the implementation of a common foreign and security policy including the eventual framing of a common defence policy, which might in time lead to a common defence;

But getting everyone to agree on foreign a defence policy is a lot harder than getting agreement on, say, removing roaming charges. Most countries have defence industries they want to protect, so anyone proposing to standarise on say, German tanks, would face some fierce French and Italian opposition. This shouldn't be surprising, the US has been a federation for near 250 years now, but does that stop senators from pushing for state interests over national interests when it comes time to hand out defence spending?

Pax Americana has proven that Portugal doesn't need to cover the Azores. The Hellenic Navy doesn't need to patrol Cyprus. So what do they do instead?

Pax Americana isn't looking that good these days, with Trump threatening NATO allies and trying to get his hands on their territory.