Others include sales, politicking (or "managing up"), managing a team, empathy, oratory, etc.
The best technical minds don't necessarily want to become suits (I'm going to avoid using the term "managers" since engineering managers are very different from "suits" imo). Even if they become one, they may not have the negotiation skills or willingness to smooch that is required for a suit to succeed.
>how is it possible that all the smart people: 1. aren't managers. 2. aren't able to convince the "idiots".
For #2, a good counterexample would be, "the best athletes aren't always the best coaches".
I'm not saying you don't need managers, or that no such thing as good managers exist. I'm just stating my observation that more often than not, who gets into management is based on the Peter principle, rather than how 'smart' or capable someone is.
I guess you must have worked for completely different companies than I did, because in my experience it's not the smartest people who work their way up into management, just the loudest ones that don't have any specific skill that would make them hard to replace elsewhere.
IMO the smartest people I know at my workplace are the engineers who manage themselves into a position where they can work on interesting projects without getting dicked around by managers distracting from the real work all the time, and make a good living doing it.