Sure, hence jab about European Army. A coalition of countries that can make Airbus should be able to cobble together functional defense. Or semiconductors, or indigenous tech platforms to rival silicon valley. They just haven't. I personally think EU just hasn't been pressured hard enough to try sincerely, but I wouldn't rule out that maybe EU is just systematically incapable.

A common defense is a big integration step.

The military is the strong arm of the political power. Giving a military branch to the EU would seal the deal in terms of creating a federal state.

This is why such initiatives are very limited and often more symbolic than anything else (e.g. Franco-German units) because sovereignty and control are very tricky matters to handle.

Then some countries, notably Germany, have issues with military power for historical reasons.