Since when viewers really think about hero breaking laws when the hero is fighting a villain ? So, by your reasoning if Batman gets government approval, he can kill ?
Not many DC heroes work for Government, so your point is ?
Also, being on the right side of the Law does not make you immune from committing mistakes, which can happen regardless of the fact whether a hero is sanctioned by the authorities or not.
You're attempting to reduce all "heroes" to the same governing traits and rules.
These are each different characters, with different character traits, and working under different circumstances.
The moment someone attempts to reduce the matter of, specifically, Batman killing or not, to whether or not a GOOD GUY kills, you've stepped outside the entire discussion.
If you're going to attempt to compare anything remotely resembling apples to apples, then you have to look at characters within given bounds.
You can compare characters who have traditionally been associated with explicit no kill rules, like Superman, Batman, Daredevil, etc, on the grounds of comparing their respective rules, and how fast and loose they may or may not play with them, etc.
That doesn't mean you cannot compare Batman to Captain America, but you can't just make blanket comparisons on the use of lethal force.
Bringing up the likes of Captain America introduces matters like acting as a government agent. That's NOT saying that heroes and vigilantes can only kill if federally employed. It's saying that it's a different condition.
Also, Batman, acting in the position of Cap, for the government, would STILL refrain from killing because it's a matter of his CHARACTER, not his circumstance.
Other characters would NOT be so hard set in their rules. We've seen Superman break his no kill rule numerous times, including killing Zod, in the comics. I don't recall if it HAS happened, but I imagine Spider-man would also be much more willing to cross that line out of what he felt was necessity, or in self defense with no other option.
Characters for whom this is already an established flexibility, or at the very least not such a central core tenant, are much easier to play fast and loose with in adaptation.
While there WOULD be outcry if Spidey spent his film fatally disposing of thugs left and right, if he lets one or two die in the course of serving the greater good, people aren't really going to complain (as much.)
Also, the current market informs the reactions as well. In today's "saturated" market, there is much more expectation of faithful adaptation. Hence why people tend to look slightly LESS critically at Burton's psycho Batman, than the Bat-Murder of Bat-ffleck.
With Bat-ffleck in particular, the criticism is also compounded by the fact that we just had an entire trilogy (and one regarded as some of the best CBMs ever) that was VERY explicit about his 'no kill' policy.
