The "battle" from TUC is really easy logistically. You've got an invisible enemy attacking Our Heroes and constantly moving so that Our Heroes can't hit it. Chang takes his time because he's a jerk and has no reason to think he's in any danger (classic Bad Guy move).
Or then he's desperately trying to hide the fact that his ship is an assassin's Derringer and no match for Kirk's assault rifle of a starship, by pretending to fire wounding shots out of sheer sadism.
Chang's weapons were supposed to convince everybody that they came from a Starfleet ship. They probably were provided by Cartwright, then. But they were only ever meant to wound: if they accidentally blew up
Qo'noS One, there could be no footage of "Starfleet assassins" gunning down the Chancellor. So it might well be Cartwright only ever gave Chang wounding torpedoes, not lethal ones...
Sprouting Shakespearean insults at Kirk would be a shrewd tactical move, distracting our heroes from the fact that Chang's ship was actually a pushover and that
any maneuver other than trying to fight her would be tactically superior. If Kirk realized Chang's worst could only ever tickle the
Enterprise, he'd simply fly right next to the planet, drop shields and beam down. But if the thought Chang could kill and was holding back solely because he was batshit crazy...
I wouldn't have minded if Kirk had at least fired weapons a bit more with some hope of randomly hitting the BoP, but it works well enough without that.
It's also pretty realistic to assume he would have hit nothing - the odds would be immensely against that. But there are obvious dirty tricks that he could have tried, wholly in the Trek context: blowing techno-smoke and seeing if the BoP left a hole in that, laying mines to limit Chang's maneuvering options, attempting exotic types of scanning rays. Were this the 24th century, he would have tried those. And it's a good thing we can interpret his inactivity as a sign of times, of his ship and crew being incapable of whipping out an Inverted Decathron Ray or a Isostatic Space Powder in a matter of minutes.
I like that the existence of the sensor equipment is even foreshadowed early in the film, though it's a bit of a goof that it's mentioned with regards to Excelsior, not Enterprise.
But it's also a Meyerism, a reference to the International Year of Geophysics where superpower navies carried "scientific" equipment to all parts of the globe in order to better spy on each other. Every ship would supposedly have the spying gear, even if only the
Excelsior dared bring hers to the very doorstep of the Empire.
Timo Saloniemi