Well, it depends who you are at war with. If Russia was rolling tanks through (more of) eastern Europe WW2 style then just out of self preservation other EU countries would want to commit forces to defend against that.

Helping France keep control in Africa somewhere I can see there being less enthusiasm.

Also, I'm not so sure European identity is receding anymore, although that narrative is of benefit to other large powers.

To me this reads like an argument centered on an idealised national soldier.

People join the military for multitude of reasons, including just to have a job that isn't working a till. No one is joining the French Foreign Legion to die for France, no one joins a mercenary company to die for stock holders. It's a job, yes for some it's a pure calling but often more than not, it's a place to work and pick up new skills.

>People aren't willing to fight and die for the EU, not in large numbers.

As has been the case for the vast majority of wars throughout human history.