Having tried to phrase my earlier questions as even-handedly as I could, I'd now like to do some opinionizing.
It boils down to this: letting humans -- whether players or GMs -- determine whether someone can gain or keep one of the high-status rewards in a game is always going to be considered to be subjective. It's always going to have to be defended from charges of unfairness.
On the one hand of promotions, some of those who aren't promoted are going to resent being passed over. Certainly that's how things go in the real world, but in a game there's vastly less peer pressure against complaining about the slight. In the world of games, in fact, complaining loudly and constantly about perceived unfairness is commonplace.
Furthermore, if it's players who decide who gets promoted, I have to reiterate my earlier question: how do you design a player-determined membership system such that it can't be captured by a group who only let their friends become members?
And on the other hand of demotions, the question of personal subjectivity looms even larger. Now you're not just talking about not giving somebody a treat -- now you're actually taking something away. Gamers hate that. Even the most trivial changes for the good of the game get called "nerfs" and are described in terms that would make you think the developers personally hate the player and want them to suffer... so imagine the response to being demoted without consent from a general officer rank.
The thing about automated systems is that a computer program is generally perceived as completely objective. Once the rules of the game are implemented, everybody lives under the same rules. If you do X, Y, and Z, you get promoted to Admiral; if I do X, Y, and Z, I get promoted to Admiral. That game would be considered fair because everybody has equal access to the same reward. "The game" doesn't play favorites.
That doesn't mean driving every bit of gameplay by inflexible rules is always desirable. Gameplay doesn't become perfect just because it's made explicit as code. For example, if you do something bad to me several times, I'm eventually going to realize it and stop letting you do it. But a piece of code is considerably dumber than a person; it'll let you perform some game-injuring exploit over and over and over again. So just because some reward system uses an objective method of scoring doesn't necessarily mean it's better than a system based on human perceptions. (There are important reasons why we don't just replace all judges with computer programs.)
That said, a reward-provision feature is generally going to be more trusted when implemented as impartial rules-based code than when it's left up to the subjectivity of humans.
So while I appreciate the concept of letting players or GMs decide promotions to and demotions from the rank of Admiral, in practice I have serious reservations about that approach. I'm not against letting players (or GMs) have some say in who they think merits promotion or demotion. But I don't think I'd want to play a game (emphasis on game) where my chances of success are drastically reduced merely because I don't suck up to the Right People.
At any rate, I hope this helps clarify the concerns I've got. I could support a promotion/demotion system in which the opinions of players or GMs were meaningful components in a clearly defined and game-enforced calculation for who can become an admiral and who (with suitable warning beforehand) gets busted back to Captain.