That's not how the military works at all. A Private is an enlisted rank, and their career path typically tops out at a level like Warrant Officer.
If you want to be a General, you're going to have to start as a Lieutenant (the lowest commissioned officer).
What proportion of officers in the US Armed Forces graduates from the military academies? A third? I very much doubt graduating from one is required to become a general. Being a great political operator is but it’s not like only military academy graduates can do that.
That's not entirely true, though as I understand it is becoming more true; there are definitely places that will promote to positions for which the normal route is a post-graduate degree based on a lesser degree plus experience (including publications under the rubric of experience).
Now, university faculty positions, degree standards tend to be ironclad, though.
There’s a way that academics come off which I don’t think they intend to - which is somehow their path is special and their trials are unique.
They’re not.
It's like if you want to be a General, you are going to have to be a Private first. There is a progression in the sciences.