The fact of the matter is that it's always adults (usually 30+) who are writing fiction aimed at young adults. Which isn't that surprising really - everyone old was once young, so we can all write relatable young characters.
One advantage that Starfleet Academy has over a lot of IP trying to focus on young folks is that you don't need to worry about pop-culture references. It's way easier to try and write relatable young adult characters as a middle-aged person if you don't have to actually know what teens are into these days. Indeed, the few attempts that Trek made to engage with pop culture in the past, like the hippy episode of TOS, were cringe, as the kids say these days.
Exactly so. Also, and more importantly, a "coming of age" style story is not exactly a foreign concept. Even if people haven't all gone to college or such, they have all had an experience of feeling like they are becoming an adult, or struggling with identity and relationship building moving from adolescence to adulthood. It might not be the same for all, but the challenges are relatively identifiable.
Starfleet Academy keeps getting treated like it's just going to be school based, which might explain the reticence to embrace the idea. For me, there are several possibilities that can touch upon with the Starfleet Academy. One, is a new recruit, who is wide eyed, interested in learning all they can possibly learn, and that excitement, even with their inexperience. You can have a more seasoned crewmember who is working on becoming an officer. You can have a student from another background, or from another academic institute with integrating different ideas into the way Starfleet does things.
Setting: The Academy doesn't have to be set just on one campus. If you look at current US NAVY Midshipmen coursework, they have a cruise that they can participate in during the summer, depending on the specialization, including aviation, or Marines, nuclear powered vessels. Here's a full list:
Naval Reserve Officers Training Corps - Summer Cruise Training (navy.mil) and would be a good place to start for ideas.
So, the Academy can be set on a ship and doing training options, working their way through a ship, from the hull up. If you want an example of this read the second book of David Gerrold's "STAR WOLF" series, and a newly assigned crewmember going through a bit of a hazing with helping out various department heads and learning in the process.
The various book series that have used the Academy as a setting often utilize cruises, and planet based assignments, as well as disaster response. It can be fun, it can be light hearted and silly, and serious and explorative. In short, it has a wide variety of possibilities that can appeal to many people, regardless of age.