Honestly, I don't think this is the appropriate way to go, either. Back when I was in high school, I used to write fanfiction, but as a rule I never wrote a fic on anything I liked. Instead, I took things that I didn't like, but saw potential in and experimented with the ideas to see where I could take them. Now, if you're willing to excuse the fact that I really didn't know how to write very well in high school, the stories ended up being decent to pretty good (with certain qualifying statements attached, obviously, they were high school fanfiction, not War and Peace).
That said, I still have to say you're wrong to think that non-fans should write sequels, because X-men 3 was written by a non-fan. Then again, so were X-men 1 and 2 and those were pretty decent. So, putting a non-fan in charge isn't the solution. The trick is to put someone in charge who is willing to explore the idea and see what can be done with it. Some fans might be willing to do that and some non-fans won't. And sometimes, the original creators will do that (the best example of this is Thief 2, which was in every way better than its original, which was already a pretty good game to begin with).
Basically, what you'd need to get rid of is the willingness to milk a cash cow with no concern for the franchise itself. That's where sequels get screwed. So, a lot of problems would be solved if executive committees were all tied to their chairs and not allowed to do anything other than provide funding to the real creators. The rest of the problems would be solved if creators would just have some fucking integrity and not sell out at the first sign of shiny objects.