So, IF we suspend disbelief, and instead give faith to the Man of Steel, that he'll forego his nice-boy deal, AND we assume that he can find Batman in a large metropolitan city, AND we believe that there's a reason he'd drop a building on him, or cook his butt wit' the heat vision, then maybe...
I still think that, given the natures presented for the two characters, Superman's too nice. It's possible for a Kryptonian, on Earth, to whup a wiley detective in stretch-pants. It ain't PROBABLE that Kal-El is gonna get mean enough. Gettin' killed didn't seem t'fix that.
His nature ain't mean enough. Wayne's nature IS.
Truth is, a comic showin' that would piss off more Superman fans than it would impress. He'd have to become another kind of man, one that he ain't, and that just ain't gonna happen. DC likes the income too much.