So let's be clear: in order to match your standard for moral perfection, we must put a ship of 1000 people in serious jeopardy to rescue a crew (unknown number) of hostile armed individuals led by a genocidal maniac, who are refusing help and actively trying to kill us, and who may or may not escape in their (damaged but still very dangerous) ship to attack another time period?
No, just let the ship sink. Very simple.
Yeah, let the enemy ship from the future armed with uber-weapons, capable of surviving a temporally-linked blackhole and crewed by fanatical, genocidal nutjobs sink ... through the black hole time portal into someone else's backyard. Let some other jerk deal with it. Not your timeline, right? Who cares?
Mealy-mouthed cowardice is not moral fortitude. Passing the buck is not moral fortitude. Suicidal niceness is not moral fortitude.
Throw out all the philosophical big names you want. Justice is irrelevent. Revenge - irrelevent. All that matters is lives. Dead people don't get to moralize and wring their hands about might have beens. The
Narada was a direct threat to both the
Enterprise and another whole reality. Kirk had the upper hand and offered Nero the chance to surrender. He declined. The battle was resumed until the threat was ended.
Kirk is a Starfleet captain, his duty is to protect his crew, the Federation and any potential innocents in harms way. That's it. He didn't swear to ensure he would sleep soundly at night, though I have no doubt whatever bad dreams he may have won't be over ordering the
Narada's coup de grâce.
In the real-world Navy, if you offer to accept the surrender of an enemy vessel which is sinking and are refused, you don't wait for it to sink - you sink it. War isn't a game or debate in an ivory tower.