Instead of going back to revamp the franchise, I think they should have done a Starfleet Academy series set after voyagers return. It would have drawn in the younger sci-fi viewers giving them something to relate to and given the fan base familiar faces and story-arcs. One episode the 'Doctor' stops by to give a speech on Delta Quadrant medication, another you pass by Prof. Miles O'brian's engineering course or Dr. Crusher's medical lab (or give a returning cast member a main character role, why not). One of the main characters could be aiming for the CONN position to throw in space cg effects every now and then, another main charater's a Klingon transitioning to earth's rules. You can even have the occasional Romulan or Borg threat or do class away mission, reaching to further reaches of space using the new transwarp system. Aliens attack and they send out a distress signal and Worf in the defiant drops out of transwarp and kicks butt.
I'd say leave the Klingons alone, we've already had Worf and his struggle to balance Klingon and UFP beliefs. The first full-blooded Romulan (or maybe a Cardassian just a few years after the Dominiopn War) at the Academy would be interesting--I'd like to see this as a female character.
You can't have cadets out saving the universe every week without jumping thorugh some pretty big logic hoops and/or straining credibility.
Wesley did it all the time.
Seriously though, it wouldn't be about big universe-changing stories, but more the relationships between characters, their own development and drive, and looking at the things from the perspective of those at the bottom (like in "Lower Decks"). All of which wouldn't be a bad thing for Trek, seeing as how the last two series were more about the evil-alien-of-the-week, resolving the situation with weapons fire, or large-breasted women in skin-tight catsuits.
Trying to get 20 episodes a year from the idea though might be a little tough, so they could try what we do over here and have each season at most 12 epidoes. The series would only have a run of 4 years, then if another series was developed afterwards then there are some potential characters to carry forward.