How would Superman fighting Batman affect the methods that Batman uses? Superman could beat Batman until he's near death every month and it wouldn't change Batman's outlook on crime fighting. Why would it? It would also just confirm for Batman that Superman is the danger he assumes he is. Superman may disapprove of Batman's methods, but he isn't stupid and he isn't someone who opts for violence as the answer. Having a difference of opinion about methods would have never been sufficient motivation for Superman to engage in a brutal fight with Batman.
The only scenario that would even work to some extent is if Superman catches Batman in the act of vicious enforcement of his form of justice, and he fights him to stop him from crossing a line and to turn him into the authorities. However, a scenario like that doesn't leave any room for the two of the heroes to come to an epiphany or understanding that evolves their dynamic into something more positive.
As it is in the movie, Batman still fights Superman because of his beliefs and Superman fights Batman in a way that ultimately illustrates that he isn't the villain Batman believed he was; thus he fights for his beliefs as well, just in a different way. Yet, because there are other variables involved, it permits the two heroes to find common ground in a way that makes a logical path forward for them as teammates and friends.
