And that could change tomorrow. You never know what the future might bring. The character changes with the times as a contemporary hero. These writers and storytellers are always looking for new ways to put their own spin on the character.
My point is, there isn't "right" or "wrong". I'm all for the no killing code. BTAS Batman is probably my favorite interpretation of all time. I grew up with the Adam West and Denny O' Neil, 60's and 70s versions of the character that were exemplary of that idea. The ones that are brutal and kill on occasion though don't bother me in the slightest. That isn't all they're about. I don't see why people get so antsy about it when there are thousands of other stories to choose from. There are articles and pages dedicated to Batman's killing/murdering history, he's done it in the past, and has done it "recently", rules be damned.
The very incarnation that started all this, the creation in which all interpretations stem from, maimed and killed without any second thoughts. Simple stories, sure, but are we really going to say that the version that started it all is now invalid and "wrong" because today's standards, 75 years later are different? I don't think so. I'm surprised we haven't seen the obligatory "he's not Batman, he's the Punisher" argument yet.
Now you're on a completely different topic than I am.
Of course that Batman can kill in other continuities such as the Elseworld stories. The 1940's comics are practically Elseworld stories and they make sense for their time, so Batman killing there is just fine.
What I am talking about is the mainstream DC comic universe, the "New Earth" universe as it is known as. As in the universe that is to the DC multiverse what the 616 universe is to the Marvel multiverse. In that specific universe, Batman cannot kill. Any attempt to try to make him kill is "wrong" in that universe (except for
maybe a once-in-a-blue-moon scenario). It doesn't mean the Earth-Two (Golden Age Batman) is wrong though. Why? Because he is in a different universe. Each universe has to play with the rules and characterizations established.
To offer an example, you and me talk a lot about how TDKR's ending is inaccurate to everything that is Batman. However, that isn't because it goes against what the Batman that we know from the comics would do. It's because we believe (I say that to not start any big debates over TDKR at the moment because we've had too many already) that it goes against what
Nolan's Batman that we know from the previous movies would do. It just happens that Nolan's Batman was so immensely influenced by "New Earth Batman" (the main version of Batman we all know) so thus TDKR's ending goes against happens to go against both versions (again, in our view - to not start any TDKR debate at the moment). TDKR's ending is "wrong" in that universe. Batman being fooled by Talia's deception despite what we see him do in BB/TDK is also "wrong" in that universe but these things wouldn't be wrong in a different universe. Heck, those things could be 100% right in a different universe despite those ideas not being my cup of tea.
Any universes heavily based on the "New Earth Batman" (mainstream Batman) is also included in this. This includes adaptations such as the DCAU (Batman TAS), the Arkham universe, and the Nolan universe. All these universes based their Batman on the New Earth Batman of Post-Crisis comics - the Batman that doesn't kill. Thus these versions are all very similar in character and all have the no-kill rule, something they each establish right at the beginning when these respective creators - Bruce Timm, Rocksteady, Nolan - created their respective universe. Therefore, Nolan's Batman killing Talia in TDKR is "wrong" in his universe, especially after establishing the no-kill rule throughout the 3 films. Him leaving Ra's on a train to die - despite it not being direct murder IMO - is still out of character for Nolan's Batman. I can't see Nolan's Batman doing that based on type of person he is.
And finally, no, all of that can't just change tomorrow - at least not in a non-Elseworld story. First, there would be tons of fan backlash (and rightfully so). Second, as I said before, Batman became a more interesting and more complex character in the New Earth/Post-Crisis/mainstream/616/whatever-you-wanna-call-them comics (this is, once again, excluding Elseworld stories not in the main DC universe) so taking him back to his "Punisher roots" would be a stupid idea in the first place. And third, as I said before, the Batman we all know from today's mainstream comics is defined by his no-kill rule in a way that no other superhero is. Due to that, it would have a larger affect on his universe. For most superheroes, altering their no-kill rule wouldn't really affect their universe in the long run. For Batman, it would.
Everything would be completely different. Nothing would be the same. No relationship with his supporting cast and villains would be the same. His relationship with Joker wouldn't be the same. The purpose of Robin would no longer be needed and wouldn't be the same. Ra's and the LOA would almost not be villains. His relationship with Gordon would be different. So much would be different.