Did they go in to why they kill, have an actual discussion on which method super heroes use is better and view the merits and draw backs of them, or did they just resort to beating each other up over the issue after turning a shades of gray issue into a strict blank and white issue?
There's a montage of Superman looking at the effect the Elite killing their opponents has on society, and he sees how the morality of people is shifting. At the end of the montage, he sees a couple of kids, one dressed as him and the others dressed as the Elite. The kid dressed as him complained that it's unfair that he can't kill the others, but they can kill him, to which another kid tells him to let them kill him so he can be someone slse, a notion the kid in question jumps at.
It showed that superheroes are heroes, people look up to for moral guidance, and when superheroes say it's okay to kill, that comes at a price.
The Authority on the other hand did not bother with questioning its own methods. Which is especially jarring, since there's an issue of "Stormwatch" during Warren Ellis' run, where Jack Hawksmoor is shown in a moral dilemma, because he's ordered to kill a villain, something he's reluctant to do because it goes against his personal moral code. But in the very first Authority story, he quips about how he's looking forward to break someone's head. That was the same character, written by the same writer, and his moral code was turned 180° without explenation.
And don't get me started on the whole "if the hero kills just one villain ever they will eventually run around indiscriminately killing people" bullshit that makes "no-kill rule" heroes look like barley control psychopaths looking for an excuse to slaughter everyone.
Superman has killed Zod and his two mates, which was discussed earlier, and he came back from that. Wonder Woman killed Maxwell Lord and came back from that. Hell, even members of the Elite were later rehabilitated and became member of "Justice League Elite".
So, no, I'm not one of those people you describe.
On the other hand, I kinda read something between your lines. Could it be that you are actually in favor of superheroes killing, that you are one of those fans that "What's so funny about Truth, Justice and the American Way" was a reaction to? I could be mis-reading, but that's how you come across to me.