Isn't it for the best, though? I don't want a Superman who would fight another man -- even to the death -- just because of a difference of opinion when it comes to crime fighting or because he thinks Batman is too hard on the criminal element. I think this is meant to be a direct challenge and parallel to the fight with Zod in that Superman would want to avoid engaging in a potentially collateral damage creating brawl that could, in this case, legitimately hurt a mortal man.
Lex only gets his "fight night" because he uses Superman's humanity against him -- the exact thing that Batman and the public fears Superman lacks. The only way that Superman will even put up a fight that could potentially kill Batman is because he has people he loves at stake; otherwise, he would hold back due to his own moral imperative. I like that, and it works a lot better than fighting over ideologies, since you can't kill ideas with violence.
A fight wouldn't change either of their perspectives, and Superman would only prove Batman right if Superman willingly fought him to the death just because he didn't approve of the way Batman dealt with crime in Gotham or he didn't like that Batman disapproved of him. He would be proving to Batman that he's a god who would get his way by force. Superman only fighting because he's being pressured to do so for reasons that are appealing to his heart and his humanity allows for Superman to do what a ideologically motivated fight wouldn't, which is to ultimately move Batman to see Superman's humanity and vulnerability. It allows them to transcend their differences in a way that sets them more effectively on the path to bond as teammates and friends. A mere fight because of a difference of opinion wouldn't have accomplished that, I don't think.