I’m not sure it’s true that being a bad middle manager makes you a bad director or exec.
I definitely agree that the most effective upper management (directors and execs) would mostly make terrible middle managers.
Idk how you “prove” you’re anything beyond middle management anyway as an external hire outside of network tbh which is maybe why some of those positions go for over $1M/year which equally boggles the mind - to cite an example, why is an HR director at Netflix making $1.2M/year