Kamui has not only put other people in the hospital, I imagine he's gone once or twice himself because he likes to fight. A lot. A lot a lot.

Also, in canon he teams up with a manipulative schemer as The Brawn(TM) so that could potentially become a thing in game too! He's actually very easy to manipulate because he doesn't care about the reasons behind things; if Alex's machinations mean Kamui gets to fight someone strong, he'll happily go along with them.