You greatly understate EU defense dominance. Ship building, subs, tanks, semi-autonomous weapons, small arms, self-propelled artillery, etc., are all areas where EU member states meet or well exceed US/UK weapons exports, particularly Germany and France. Although not an EU member, Turkey is increasingly becoming a player in the drone, small arms and missile space. Its easy to confuse high profile programs like the the F35 with the much greater volume of other categories of arms.
You can add aircraft (yes, there's no equivalent for the F-22 and F-35 but both don't form the backbone of the USAF yet and cost an outrageous amount of money), and helicopters, rockets, radar/sonar, combat systems (Thales is a world leader in that sphere) to that list.
> Maybe EU should keep some weapons for itself, instead of exporting everything:
They got the message. IIRC, Germany's going to throw something like the equivalent of two years worth of extra defense spending at addressing its military under-funding problems, plus actually meeting its NATO obligation of 2% GDP in defense spending in the future. IIRC, there was even talk about making that a constitutional requirement as well.
