Some people have suggested making command of a starbase a perk for leading a large player organization. (Let's follow accepted usage and call them guild leaders.)
But why would an experienced guild leader want to command a starbase?
Let's say we've got someone who's been a great guild leader. They've pulled together a lot of different people to get a lot of things accomplished in the game. They've done a lot of exploring, a lot of socializing, a lot of combat... probably a lot of combat. Their existence in the game has been one of going and doing; they've been highly active in bringing people into the group and making membership in the group fun.
And their reward for that whirlwind of activity will be to oversee a stationary support function? To spend their time making sure that other people's ships get fixed so that other people can go out into the galaxy to have active fun?
I'm making the assumption here that the primary function of a starbase is support, rather than direct gameplay action. Yes, if a starbase is attacked there could be some action, but it'll be defensive, not offensive -- and it won't happen all that often. (It better not!) Which means that most of the time, the point of a starbase will be to supply services to other players who are going Out There and doing exciting things.
Is it really likely that this is the kind of reward for services rendered that a highly active gamer is going to enjoy?
People want rewards that let them do more of what they enjoy doing, not less. Rather than a "reward" that radically changes their gameplay, action-oriented players need action rewards; exploration-oriented players need rewards that offer a higher level of exploratory play... and social players need rewards that let them socialize more. Such as commanding a starbase, whose function is to stay in one place and help lots of different people.
I wouldn't expect the leader of a gung-ho, action-oriented guild to enjoy it if the reward for all their activity was to oversee a stationary starbase, any more than I'd expect a cooperation-oriented social player to be happy if their reward for being a great social player was to lead a bunch of ships in combat or do behind-the-scenes strategic planning.
As a rule, high-level content shouldn't change the type of game a person enjoys playing. What it should do is give them even more of the specific kind of gameplay they enjoy.
And note that this "more of what you like" approach is what I propose in my "Combat Modes and Player Ranks" essay for each rank. As players find the kind of gameplay they enjoy, as determined by their rank, they're able to increase their level of competence in that rank so that the level of challenge increases with them. The difficulty increases while the type of challenge remains the same.