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Peter is gotham, fine and dandy, all the tropes you could ever want BUT
Into the spiderverse right. With The Canon explanation
So picture Peter falls into DC, and his canon ties to his own universe are cut because his canon was essentially erased, comic book logic and all that
So DC (or sentient Gotham!) Basically adopts Peter into their universe, and also his canon.
What does that mean, you ask?
PICTURE THIS.
Peter now has to live through everything considered a canon even for a Spider-Man, including but not limited to Uncle Ben's death. This works beautifully when paired with Jason being Ben's equivalent, like a fine wine and cheese