The main plot of Jedi Academy is nearly superfluous. There's this cult that's going around and somehow draining the Force from certain special locations, but that doesn't concern you directly. With masters like Luke Skywalker and Kyle Katarn distracted by this sinister plot, it falls to trainees like Jaden to pick up the slack and do all the regular Jedi missions - investigating crashed spaceships, arresting crime lords, rescuing hostages, that sort of thing.
I actually like this setup and think it would have been interesting if the game had ditched the main plot and just gone for a pure "day in the life of a Jedi." After all, when your job requires thrilling heroics as a matter of daily routine, you don't really need a galaxy-spanning conspiracy to spice things up.
This gets me thinking about other games that have similar issues. Take something like Mass Effect, where there's this big, apocalyptic event that you have to investigate and thwart, but along the way you get dozens of "side missions" where you do lower-level space-cop stuff. The usual plot critique is that it makes no sense that someone on such an important mission would take time to divert to a backwater planet and chastise an unrelated drug dealer. The side missions are a distraction from the main story. But now I wonder if, perhaps, this is backwards. Maybe the main plot is a distraction from the side missions.
Video games have a unique ability to transport you to a new world. They give you things to see and places to go and characters to interact with and it's interesting to see the relationships between these things. Even in poorly-thought-out settings, there are still relationships in physical space. This thing is over here and that thing is over there. There doesn't need to be a story. The real world doesn't have a main plot. A virtual world could be the same way.
But then again, I am a big fan of survival games, so maybe I'm biased. I guess the takeaway from this is that I wish Jedi Academy had more side-missions, presented in a more organic way. Maybe instead of selecting my next mission from an interstitial menu, I could take time between missions to explore the Jedi Academy and perhaps get my missions from the various characters still stationed there. That's the way they'd do it today, though I guess 2003 was a different time. Open worlds were not yet obligatory. Nonetheless, I like what I got and am happy to keep playing it.