I guess it will sound like a nitpick, but to me it matters a lot:
They promote those they believe have the highest potential to bring value.
The whole thing is that the person who promotes you is a human in a dominant position. You can't change their mind about what they believe is a good reason to promote an employee, because they are in a position to feel superior.
If you want a promotion, you have to do whatever those with that power want to see in order to give you a promotion. If that involves bringing doughnuts every Monday morning, you have to do it.
Luckily, cargo cult means that those people probably all read the same kind of books, so a valid proxy may be to just read those books and try to fit in this completely arbitrary world. Coaches are people who decided that instead of reading those books to try and get a promotion themselves, they would just make a business out of reading those books and selling you that knowledge.