I used to be adamantly against fan fiction. The idea of taking an already well known story and writing your own take on it seemed wrong to me somehow. Writers should create new worlds, new stories, and new characters instead of just relying on someone else's.
Then, I began thinking of this in a different way, and my opinion changed.
When I was in art school, we studied the greats. Part of that was doing master copies. We'd choose a painting by someone we greatly admired and attempted to copy it to the best of our abilities. I spent hours pouring over books and staring at masterpieces in museums. This exercise allowed us to not only discover how they made that piece but how to riff on it. We could make it our own a little, and thus, were a part of it somehow.
In music, you see the same thing. Would Adele covering an Aretha Franklin song be considered the same as my old definition of fan fiction? No, it would be considered an homage. Musicians take songs they admire and put their spin on them not only as their own expression, but out of respect for the artist who originally performed it.
Film is no different as is performing arts. Any director, actor, or dancer will tell you about their influences and mentors. I've never heard any performer say no one inspired them. No one's work impacted their own. This is how styles and genres are defined and expanded upon.
Fan fiction in the writing world is more of an homage. This is the realization I've come to. Of course, there are good and bad versions of this, and plagiarism should never be tolerated. The thing to consider is every piece was deeply inspired by someone else's work, and they sought to create something they thought was beautiful from that inspiration. To build off of someone else's world is an active practice of admiration.
Look at Wicked, both the musical and the book series. This is considered fan fiction, but what an amazing form of it. Gregory Maguire took a story that is internationally known and celebrated, and he made something beautiful and unique by showing us a different take on the story. Everyone knows the story of Dorothy in the Wizard of Oz, but he takes a darker view of the whole thing from the Wicked Witch's perspective.
My one caveat to all of this is, and of course this is just my personal opinion, if you are a true creative, you shouldn't live completely in the homage world. Pay tribute to the ones who inspired you, but then create work that is just yours. After all, that's how the next generation gets inspired.