I get the Green Arrow example, but there's more to it, I think. Yes, there's the continuity issue, but that's fine if you just say that "hey, things change" and move on. You're right that it affects everybody else indirectly, but that's not all that's going on.
(We also agree, I think, that in the service of a good story, you're allowed to be somewhat inconsistent, both in continuity and morality.)
The most glaring thing I saw when reading the Grell series, though, had nothing to do with what the JLA thought of him. It was that someone who's so outclassed that he "needs" to maim or kill to survive has no business carrying around a longbow and dressing like a Keebler elf. You can't introduce a measured quantity of "realism" and expect the remainder of the four-colored world to be a viable backdrop.
In the real world, if you need an advantage over an opponent and you don't have trick arrows at hand, then the bow is simply not an appropriate weapon. It'd be like reimagining Wolverine to carry a Swiss Army Knife instead of claws--treating it realistically is going to outright hobble the guy.
To me, it's also not about the power level. Is it OK for Superman to kill, just as long as he's overwhelmed? What if it's an even fight? What if they guy looked tougher than he actually was? What if he's emotionally overwhelmed, rather than physically? If any of these, doesn't it just mean that Superman gets to kill whenever the writer feels like it? What other parts of the writer's "contract" are only at the writer's fiat?
Actually, I have a counterexample to the Green Arrow (and Pulp) example in Tom Strong. The literary boy hero, I mean, not the Alan Moore thingie that I've never read. In the first book ("Washington's Scout"), Tom joins up with the Colonial Army and participates in multiple battles, rifle a-blazing and (presumably) racking up a pretty big count of dead bodies. He's fourteen, but it's wartime in a realistic book, so we expect a certain amount of acceptable carnage, and don't hold him to special morality.
Except...about midway through the book, he and his (adult) sidekick capture a Hessian sentry. When the older guy is about to slit the German's throat, Tom makes an impassioned plea to save him, because killing is wrong.
Again, note the problem: It's OK for Tom to shoot enemy soldiers, but it's somehow not OK for him to stand by while an allied soldier kills a single enemy soldier. The situational morality (which is what this really is--the rules are different on a literal battlefield) looks like absurdist hypocrisy, considering that the sentry is every bit as dangerous. What makes those two situations SO different (other than the Hessian needed to play a significant role later in the book) where Tom is sensibly right?
As you probably already know, Mason wrote this over a hundred years ago, predating the Pulps as we expect them. Sure, it's kiddie-lit, but it's still a useful data point, I think, because it certainly inspired them.
Along more Pulpy lines, I'll also note Jimmie Dale, dating back as far as the 1910s, who carries a gun everywhere, but never uses it AS a gun. He'll threaten with it (Zorro-like), club people over the head, and even use the muzzle flash to see in the dark, but in all five books, I can't think of a single instance where he fires a bullet at anything, and he spends all five books fairly thoroughly overwhelmed by mobs of thugs.
Keep in mind that I'm not arguing the point. These are personal and aesthetic judgements, I think. There are people who believe that killing isn't a particularly bad thing, and there are people who believe it's the absolute worst thing anybody can do to any living thing. My main point is, essentially, that heroes who kill inherently violate their own premise, and it doesn't matter how many excuses are supplied by the writer. It can be done well enough that nobody cares, but that's much harder to do.