First we need to determine what fan fiction is, if its using the same world/mythology/characters as a previous work we’d have to toss out American Gods (fan fic of gods in modern setting), Good Omens (fan fic of Christian Apocalypse), the entire Percy Jackson collection, Röde Orm, and the Kalevala just to name some
Edit with a big example:
Der Ring des Nibelungen is a fan fic “musical” written by Wagner of the Nibelungenlied
So where do you draw the line? I don’t know where the line would be so I’d rather not ban fan fics at all since I can see why those works I gave example of contributes to both the literary world at large but also as ways to tease imaginations and reading lust in younger or unselfsure readers (English is my second language and I’m not sure if I used to correct term or even a proper word at all in the last sentence)