Admiral Vance is the exception, yes, but not running the academy, just there to smile at the captain’s quirky behavior.
What if I were to tell you that Ake is just there to dole out tough love to Caleb? He's the show's protagonist. Others may have their arcs, but they'll ultimately bend around his story.
But Vance is the one who gave Aka the job, and ran the negotiations in the second episode. He's had a more prominent and varied role than any of the women under Ake's command so far. And you're still ignoring the EMH, Ake's CMO and our heavily advertised legacy character. You're not being very honest in your arguments so far.
And you're saying it doesn't make sense for a woman to be in charge of something? Even if there's a prominently featured man both above and below her in the chain of command? And men at the same relative level in other divisions? Do you just not accept Star Trek's premise of an egalitarian future? I'm not seeing how my initial characterization of you was wrong.