Because I think the framing limits what you can do. Your characters are going to be mostly centered at the Academy, not on strange new worlds, boldly going where no one has gone before. Therefore, the conflict and drama is probably going to be interpersonal about romantic relationships and family drama. That's fine. But it doesn't open up a lot of possibilities beyond that.
Not a bad point, but it'd hopefully be more than just a repetition of a shiny new alien invader trying to take over Earth, which definitely would get redundant and stupid too quickly. But it's the academy, just have some of the ensemble go out for training missions, field trips, and so on? Especially with modern shows being 8 to 13 episodes per season instead of 26, and each season is 18~24 months apart...
Remember "A Matter of Honor" and later stories that revolved around "student exchange program... in space"? Well, that can be done here. Have a couple episodes focused on one character.
The occasional alien abduction issue wouldn't come amiss, but they'd have to one-up the trope and, the last time I recall the trope being used, it was in TNG and "Schisms" wasn't all that stellar of an episode... but being centered at a static location (academy barracks whatever) instead of a dynamic one (the Enterprise), it'd probably be easier to buy into.
Did I mention that not all of the academy students are all going to be Wesley Crushers? Not sure what's worse; if none of them is, or if all of them are...
Deep Space Nine (DS9) also started out about a confined space. Granted, it's the edge of the galaxy by a wormhole where aliens of the week can come visit, bicker, and/or take over the station... but the creators definitely added in a lot of character backgrounds and archetypes and, what seemed like a limited premise, had a ton more mileage than what people were thinking of at the time...
...then again, DS9 also realized it had to expand its lore as well and finally included a ship - the USS Defiant - albeit with some creativity as to how they brought in the ship, a prototype specifically designed to be built to battle the Borg but having issues that had the ship class kiboshed, with - in turn - Sisko turning a lemon into lemonade and that's what I loved most about the ship's introduction - how Sisko kept being creatively thinking... (Apart from when the writers forget that the ship will tear itself at maximum warp, so look up its maximum warp and forget that number for when they actually state "Engage at warp (maximum number). After all, the 1996 TNG flick through everything about the Defiant out the window too... But O'Brien can easily put in a throttle limiter to compensate, since nobody can tell the difference between warp 9 or warp 6 when looking out the window... now there's some headcanon, complete with the proverbial dandruff...

)
Beyond that, how many conspiracies within Starfleet are we going to do until it becomes redundant and stupid?
TNG had set some seeds in "Coming of Age", leading to fruition in "Conspiracy". DS9 had - if I recall correctly - "Paradise Lost". TNG also had that flick of "Insurrection", which could have handled Starfleet doing something evil a bit better... but it's a new production team now and a tad over a couple decades later.
If you wanted to do coming-of-age, it would make more sense to me to do "Starfleet: Year One." Basically, follow a main character in their first year after graduating from the Academy and build a show and characters around them acclimating to being a Starfleet officer.
Not a bad idea; especially if characters in ensemble shows aren't always fleshed out right...
Chances are, there's also the old contingency and/or joke about it being "teenage romance drama... in space" is the usual standby, of course... let's see 'em shuck off the clothes, boink like bunnies while showing as much sweaty skin as possible - especially for sweeps week (if those still exist), and focus on the ship. You know, their sex lives instead of a ship to explore strange new worlds with.

Also, since the tangent is too tempting,
I
adore that scene. Even the shoulderpads - definitely am glad they didn't discard those by 1994, they work for the Romulans well and, indeed, are iconic...