I don't mean the flag officer is chosen randomly in a a lottery or something. I mean that their particular military organization is not the main factor, but their past service and previous positions of joint leadership are why they are chosen.
But you never know, maybe the committees in charge of selecting flag officers is pro-Navy right now, which might explain why a majority of those major commanders are Admirals.
Midshipman Third Class
Trojan Battalion NROTC