I don't know how you can add motorball and have it "add to the story", but I think they integrated it pretty well by tying the supporting cast to jobs revolving around the sport. I've gone back to re-read the comic and I'm still in the first motorball volume, and I noticed they even dropped a couple Easter eggs in the movie, like namedropping Jashugan and showing her racing body. It's honestly just there for the spectacle, like Quidditch in Harry Potter, but it worked for me as an action setpiece. It does add some action and thus removes some heavy atmosphere to a point in the story that probably should have been heavier, but across the board the film just isn't that heavy.
And to your spoiler, He's been toned down a lot to fit the teen girl narrative. His motivation is not strongly defined, and he is just a general "parts jacker" (not spines). He also has to deal with having reciprocal feelings for Alita, whereas in the manga it's all one-sided.The story ends up playing out very similarly, but the context leaves you feeling very differently, if I can say that in a non-spoiler way. I don't want to say that Cameron and Rodriguez missed the point, but they definitely changed the message.
This movie basically follows the anime storyline, including the character Chiren, fleshes it out with more stuff from the manga, and sprinkles in motorball. Very little could be considered original, but it's all been mixed around and tweaked to make everything fit together.
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