I hope you don't mind me adding to this very good post, but in general i think the financial supremecy of movies and (more recently) tv has lead a lot of people to assume that the best stories can be interchanged between mediums. That every book can be adapted into a movie, every light novel into an anime, every movie into a video game etc etc
and that's the same attitude that underlies all the 'the goal of fanfic is to file of the serial numbers and publish it' or 'fanfic isn't real writing because real writing is novels and fanfic is usually structurally so different from a novel' type of takes come from.
this assumption that the medium is largely coincidental to the story being told
when that's just not true.
the very best adaptations always change things, because mediums are not interchangeable, and they fundamentally shape the stories told in them.
there are things you can do in fanfic that are simply not possible in a traditional novel, because you're starting from that possition of love and knowledge, and because you aren't bound by the need to be canon compliant, so you can ask questions like 'if these characters met in other lives, under different circumstances, what would they be like? how different would they be? how much of what makes them them is tied to the circumstances they found themselves in?' or 'what was it like to not be the heroes, to not be actively involved in the cool exciting bits? what was it like to be a minor character, left behind to deal with the consequences' because your audience is already invested, they'll show up for questions like that in a way a movie or novel or tv audience wouldn't.
there are things you can do in a podcast or radio play that are not possible in visual mediums like film or tv, because you're relying on the audiences imagination. there's a reason the best radio comedy tends to be surreal, and the best podcasts tend to be horror, those are both genres that thrive when the audience's imagination is allowed to fill in blanks.
there are things you can do on TV that are not possible in a novel or a movie. the way WandaVision completely changed its visual style with each episode is something that would not work in any other genre, but it's essential to the story. TV usually exists in very defined seasons, but cannot traditionally be consumed all in one go, which is not true of almost any other medium, and that dictates a specific type of pacing. combine that with the fact that it's a visual medium, and you get something like the overarching stories of the 9th Doctor's season of Doctor Who. No other medium could have delivered the resolution to that storyline as effectively.
Video games can force the audience to consider their own part in events. No movie could do what Spec Ops did, when it gives you a button prompt to commit a war crime, and then turns around and asks you why? why did you do that? was it too easy? do you think it felt like this when the US government committed the exact same war crime within living memory? Was it easy then too? A novel or a movie could show you walker doing this terrible thing, but it could never convey the point with the same effective simplicity, and it could never make you the audience feel culpable. only the author is responsible for the actions of the characters in a novel, but in a game, it's the audience who bears that responsibility, and that allows for moral questions other mediums struggle to effectively convey.
Comics can tell stories that take three decades and ten different writers to tell. Movies can use silence more effectively than any other medium because cinemas give you a captive audience and close-ups means you can reliably assume they can see everything that's happening (unlike theatre, which can use silence, but can't assume everyone has a good view). Theatre provides real time audience interactivity and a very special and unique kind of suspension of disbelief. Professional wrestling can tell ongoing stories in real time over years or decades, and walk the line between fiction and reality. Novels can immerse you more fully in one person's view of the world than any other medium (which also allows for information to be hidden from the reader without it feeling cheap the way it can when a movie does the same thing). Live oral storytelling allows the story to be adapted on the fly to fit audience reactions, allows for infinite variations of the same story, because no two tellings will ever be identical.
Fanfic isn't a genre, not really. Fanfic has genres, but it isn't a genre in and of itself. Fanfic is a medium, and like all mediums, it offers storytelling tools that are unique to it, that it does better than any other medium. and as OP pointed out, one of the big ones is that it can assume both familiarity and love from the audience to the characters depicted. We can stray far further afield from where we started in fanfic than the original creator ever could, because our anchors are not the narrative, but the characters.
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