So to be clear, your argument has changed from "his interactions with and effects on other characters aren't up to snuff" into "he's just too strong?"
Being overpowered is just one component of Hayabusa’s problematic inclusion in DOA. My argument has always been that his existence has a derailing effect in DOA (for both being overpowered and not being integrated as a meaningful character), and it was made worse by how Dimensions shoehorned him into it.
I mean, imagine explaining it to someone who’s new to DOA:
“It’s about these magic ninjas from a clan that’s become the target of experiments by an evil corporation who wants to steal their ninja powers. Also they’re friends with an even better ninja from an even more magical ninja clan who can blow up demons with his mind. But don’t worry about him.”
It’s like if Spider-Man had a best friend named Jerry who has all of Spider-Man’s powers and also can fly and shoot lasers out of his eyes, but doesn’t really participate in any story and the bad guys don’t seem concerned with him. That’s bad writing.
To sum up my complaint: Hayabusa is both disproportionately powerful and has never had any real characterization or relationships in DOA. Dimensions tried to give him more to do, but it actually made the problem worse because it just made him even stronger and undercut other characters’ stories.
All I want is for Hayabusa to have some real relationships in DOA and something to do beyond reminding us that he’s a more important ninja than our ninja protagonists. Let him need tournament winnings to open a noodle shop. Have him feud with Nyotengu, who wants to both kill and have sex with him. I still like the idea that Tengu magic has vanished the Hayabusa village, and poor Ryu has to go get a regular job and live in an apartment with Jann Lee.
I complain because I love Hayabusa in Ninja Gaiden, but I think he’s always kinda sucked in DOA. But it’s fixable.