So your gripe is that a barely recurring character is used in a joke, and you didn't find it funny. Gotcha! Unfortunately, not every joke lands for every person.
It's important to understand that generally speaking, Academy standards are probably a lot lower than they used to be, the show, actually goes into this a couple times! Because, you know, the destruction of a large part of society and such. It is a school, and if the characters didn't need to learn something, they probably wouldn't need to be there.
You're generally going to find competency in the command staff/professors, and you generally do. Captain Ake is in at least one episode, orchestrating the entire episode behind the scenes, and in the following one, it doesn't say it explicitly, but it is most plausible that she also did as well. Episodes where the senior staff don't know what's happening, it's clear they know something is up, they just haven't determined what yet. I am not positive I can think of a spot where the officers in the show were anything but incredibly competent, and the show also avoids classic tropes like "the admiral is a jerk/evil", Starfleet is, in fact, led by an extremely competent and reasonable admiral.