Mark Millar’s comic book attracted some interest but the story was not controversial until it became adapted for the big screen. The idea of a 12 year old girl calling gangsters cunts and then slaughtering them was considered by many people who hadn’t even seen the film to be beyond the pale.
But that is kind of the point. It firmly establishes early on that this is set in the real world where the bad guys can win and innocent people can be killed or gravely injured, but then it throws at the viewers the traditional tropes of the superhero action movie. It messes with how the viewer is supposed to watch and enjoy the film, it dares people to enjoy stuff that they see as immoral.
You are supposed to be unnerved by the violence performed by Hit Girl and see Big Daddy as being as monstrous as the mob boss Frank D’Amico.