Robin Olds was a fighter jock, a Hollywood icon, a fearless leader who led by example in combat, and a superior commander.
So much for your theory.
Olds was promoted to brigadier general after returning from Vietnam but did not hold another major command. The remainder of his career was spent in non-operational positions, as Commandant of Cadets at the United States Air Force Academy and as an official in the Air Force Inspector General's Office. His inability to rise higher as a general officer is attributed to both his maverick views and his penchant for drinking.
Top fighter pilots ARE NOT good administrators. Sorry about that. They shoot, without hesitation. They are not the people you want running a company, or a logistics operation. Remember, for every man in the air, you've got 15 or 20 on the ground doing maintenance, getting parts, painting hangers, designing and building the next generations of test equipment.