Well question is why would EU want mass production of rockets and for what purpose?

Well, right now they lack that capability and don't show any interest in it, so why would anyone in the EU even bother working on the things that would use it, like, LEO megaconstellations (ie Starlink or Starshield alternatives)? They also miss out on business building out such constellations from other companies. Amazon bought up a bunch of Ariane 6 launches, but obviously in the long term they'll be shifting to something which can potentially be more cost efficient like New Glenn.

I guess the pride that requires them to have their own launcher has its limits.

For context, my understanding is that SpaceX builds one new Falcon 9 upper stage (not reused) every day. I doubt there is another entity on earth building a new rocket every month.

SpaceX has a large fleet of Falcon 9 reusable boosters, but still needs to build one every now and then.