The situation Superman was in - evil guy who threatened to kill everyone as soon as the opportunity presented itself is nothing new. Superman has figured out ways to deal with it without killing the guy during his 75yr run.
Gonna have to agree to disagree on this one. I mentioned about a dozen times where he's killed or allowed people to be killed in my post above, but remember that this is his first outing as Superman. Hell, he doesn't even GET the nickname until the very end portion of the movie.
He hasn't been practicing to be a hero, he ISN'T the Superman we all know and love at this point. He's basically the equivalent of Clark leaving the fortress for the first time in the 78 movie, except instead of robbers and terrorists to deal with, he's got an extremely pissed off guy who can literally destroy the world.
Human security measures aren't going to be able to hold him, there's no kryptonite to depower him, there's no kryptonian anything laying around help, there's no security bots left, everything is wrecked. There's Superman, Zod, and a WHOLE lotta squishy humans. Hell, even Emil died in the plane crash so the TOP SCIENTIST in the comics that figures out all this crap just bit it in a singularity based fireball. If he leaves for just a moment, Zod vanishes and starts playing "squish the humans", so it's not like he can up and vanish to go see if he can scavenge something from any of the wreckage.
At that moment, he literally begs Zod to stop, because if he doesn't, Supes knows he's the only thing that can stop him. He's tried knocking him out, and so far that's just caused a wrecked city and more time for Zod to suck up solar radiation and start wrecking things more easily and become that much harder to beat.
When Zod doesn't back down, pop goes the vertebra.
Again, HE ISN'T SUPERMAN AT THIS POINT. He's a kid from Kansas who is doing the best he can to keep the world from being torn apart. Maybe once he gets some years on him and some experience he can be the Superman we all know and love, but for right now, he's just coming into his powers.
Side note, I can't recall if we ever got a "cold breath/super breath" moment in the movie. Lots of heat vision, flying, and smashing stuff though.
Chris