Nero murdered billions of people. Kirk had the responsibility of making sure he didn't have the chance to murder anyone else, either by taking him into custody or by ensuring that he didn't survive another trip through the black hole.
I don't have any problem with it.
Now this argument--earlier mooted by I Grok Spock
hold water. Still, it's a preemptive killing based on the off chance that Nero will survive and a somewhat cold-blooded act.