Good point about bringing criminals to trial. But was there any discussion of the pros and cons? I don't remember that.
This was the huge choice that Kirk had to make. Admiral Marcus ordered a photon torpedo strike (Drone strike) from the neutral zone. Kirk was all over it. On the way to the ship, Spock argues that this executive order, by one man, is wrong and that the right thing to do would be to bring the criminal to trial. Kirk disagrees and goes off on Spock, to which Spock says something like "the fact that you have resorted to name-calling must mean that I have a valid point."
Later, when the ship is in firing position, Kirk makes an announcement to the crew. He wants to fire, but he looks to Spock and then back at the intercom, where he announces that he will go to Kronos to apprehend the criminal, so he can be brought back to trial. By doing so, he must now risk his life to do it. Spock stands next to him and says to Kirk that he has made the right choice. Of course, this puts the whole crew in jeopardy, as Marcus becomes incensed. It really is a huge crux of the plot.
Anyway, here's an article saying ST has lost its mission of dealing with moral issues.
I haven't read that, but this movie deals with a lot of moral issues, from Kirk not respecting the chair, how far a man will go for his friend, as well as his crew, the Prime Directive and the issue I wrote about, above.
A good contrast is the TOS episode, "A Private Little War", where Kirk and company deal with the moral dilemma of arming natives.
Klingons arm one side, so the Federation must arm the other to balance power. That was good. In fact, I took a "nerd" pic for you! The episode is in the foreground.

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