There are basically three possible types of content for an Academy show:
1) The Cadets are Starfleet's Last Best Hope For Some Reason: Our cadets are improbably entangled in galaxy-spanning / save-the-universe style punch-ups with baddies-of-the-week on a regular basis, or find themselves regularly on field trips where improbable coincidences and disasters require them to solve all the problems that the grown-ups would normally be solving.
2) The Hardy Boys / Nancy Drew / Harry Potter... In Space! Or at least San Francisco! The grounds of the Academy are themselves improbably perilous and adventure-prone and full of mysteries that need cadet sleuths to solve them. With Harry Potter in the cultural DNA now, this version of the Academy would probably be spouting BEMs from every corner (or crevasse).
3) Schoolhouse Melodrama: The Academy is like every other melodramatic college full of beautiful people in the history of television, where the cadets' major worries are Who Goes to the Party and Who Just Broke Up with McGivers and maybe How to Say No to Space Drugs. If it's the edgy variety of this college, the last one comes up a lot.
There have been successful shows and franchises built around various mixtures of those three themes. Most of them occur in the fantasy genre so that they can justify the improbable importance and perilous lives of the students by invoking Destiny or Prophecy or Chosen-ness. ST09, which used version 1 of this concept, basically did this too. So if you want to see a Trek show doing that on a regular basis, that's probably what you're in for.
There's an added bonus -- or penalty, depending on your tastes -- in that since whoever is making such a show also wants recognizable characters, the Academy in question will also be full of Muppet Babies, a more or less complete slate of recognizable characters from prior Trek shows who all just happen to be in the Academy together at the same time regardless of their variable ages and service records in their original incarnations. (Again, cf. ST09.)
For all the same reasons I would find this a terrible idea that should be killed with fire, someone else will probably love it.