Then you're not writing fanfic. You're writing original fiction with characters whose names happen to share those of the characters of the work. If the characters aren't the characters of that work in at least some sense, then it is not fanfiction. Which is why most Worm fics are fucking terrible. Yes, sometimes a gifted enough writer can still wring a good story out of it, but in the process they make it (barely) fanfiction - which is fine, but then advertising it as such is simply a honeytrap to suck in fans of the work, which brings us to the problems others have raised with leaning on fandoms.
You can write, say, Bleach Fanfic without featuring any of the canon characters by exploring the setting outside those characters. You have an undue focus on characters.
A given original work typically offers a cast of characters, a worldmap, and a physics system to work with. Often, they also provide interesting cultures. You can throw out any number of these things in fanfic, as long they have common elements.
For example, a Naruto fanfic can explore the culture of Ninja and the hidden villages, a Bleach fanfic can deal with the interesting power sets and the setting rules of ghosts, such as by following around a non canonical Soul Reaper who, of course, has a Zanpukato and practices Kido, and so on.
To say you must use the characters of canon to be a fanfic is absurd, as it proposes that a high school AU of Naruto is fanfic, yet one set definitively in the past of Naruto itself, using the geography, society, and powers of the setting is somehow not fanfic, while being in many ways more intimately tied to canon, because after all going far enough into the past ensures an absence of nearly all canon characters.
Ok A) Batman's a poor example because of how comics writing works - 'canon' is about seventy different writers' ideas of what Batman is, and some of them - the Animated Series in particular - are pretty snarky. And B) In the example you gave Bruce Wayne/Batman is still recognisably Bruce Wayne/Batman. The fics you're talking about don't have a recognisable Taylor, but rather 'generic teenage girl named Taylor'. Which, again, is fine - Constellations is a good fic, though I haven't read Go Gently so I can't comment on it. It'd be a better fic if the author either acknowledged that their character isn't Taylor and called them something else, cutting the last fictitious ties to Taylor, or flat out changed the world to be something different and told their fun, quirky original story of a girl learning about being inhabited by eldritch beings with its own room to grow.
This is absurd, continuing off the above. Yes, Taylor in Constellations doesn't act much like canon Taylor. But she is a point of divergence version of the same. She still has a father named Danny, she still lives in Brockton Bay, on Earth Bet, she deals with the PRT and so forth.
To write what you propose would either be a significantly divergent story, or else it would be a fanfic with the serial numbers filed off. We'd be replacing Cauldron with the mysterious organization, Bottle, and they'd have a woman with the power of Route To Success, which is totally not Path to Victory, and there'd be superpower providing space whales named, uh, Beings, which are definitely not Entities, and so on.
This entirely aside the Okami elements, where Amaterasu is
very recognizable as her canon self.