Wish in one hand, poop in the other, see which one fills up first.

The best majors essentially feel they have plenty of qualified (ie safe) pilot applications, so they are trying to cherry-pick those who fit their version of the "good employee" template.

Military officers often went to "name brand" schools, often on scholarships, often athletes, usually have a masters, always have leadership, management, and organizational skills. If they've completed ten years, they demonstrated a continuously upward progression in skill, responsibility, and leadership. That's all good "organizational fit" stuff. I have know civilian-only RJ drivers who had similar resumes, they generally get scooped up by majors pretty quickly too.

Mil pilots are not all chuck yeager, it's possible to be a "good enough" military pilot and still be a good organizational player. Military "good enough" is probably also going to equate to civilian "good enough". Fighter/attack pilots are by definition selected from the higher ranked primary training output, they have a very busy mission (ie lots of work and training), and almost all of them today actually do both fighter and attack missions, so really two jobs. And more aerobatic maneuver flight than most other communities. If you want to prove yourself as an aviator there's really no better way to do it. Flying your line in the right seat of an RJ and playing lots of video games on your days off doesn't really stack up (yes I had an RJ FO complain about how the fighter pilots were getting all the jobs... he felt that as some sort of "ranked" video gamer his skills were better than a fighter pilot).

As I said, civilians with similar resumes have no problem getting major jobs. Even without fighter time.