Frankly, it's more interesting to watch Batman work with limitations. I mean, it's his one straightforward moral that serves as a way to prevent him from just blowing something up or hitting the 'easy' button for someone who's as well-established a badass as The Goddamn Batman. His unwillingness to kill not only makes him think in new ways, but builds on the characterizations of redemption and turning it into hope because he always believes there's another way. Now, I'm not a huge fan of 'hopeful redemption Batman,' but it adds light to a character who is, as you may have picked up, pretty dark. I know that forgiveness is more Superman's schtick, but hope and belief in redemption shows that Batman is doing more than taking revenge for his parent's deaths. Now, I know the quest for redemption versus the quest for vengeance versus the quest for stopping the guy that you have a pretty deep hate-on for are all pretty worn out tropes, but for Batman they tend to work again. No one tests the Batman's principles more than Joe Chill. Bruce Wayne's begins his quest wanting revenge, and one of the good things “Batman Begins” does is deprive him of that chance early on, leaving him struggling to find a face to put to the chaos and violence which has hurt his life. He ends up looking at the larger picture and realizing that Gotham needs more justice than vengeance. The second movie gets to the hope part and maybe redemption will play a part in the third. I doubt it. There aren't a lot more “I Am the Night” episodes left in the Batman mythos.
Hope is a facet of Batman that I want to see explored more. I like it when hope leeches into the character. I understand that it's hard to work hope into Batman without overdoing it. It's not like he can just give speeches about hope without looking corny. If it's one quality of certain Batmen that I like, it's that they're doers, not sayers. Granted, it takes a bit more analysis to parse out their actions (though not always a full-length essay-novel), but I'm finding that it's usually worth the trouble.
I'd be remiss if I didn't mention heroes who did kill off their villains. Many people say that a hero is defined by their villains. The gritty, anti-heroes of the nineties aren't that distinct from one another aside from the source of their powers and just how terrible their dialog was. Can you even name one memorable Cable villain? That's right; Strife. Clone Cable who was deadlier than Cable was. Oh, and Time Traveling Dick-Bishop, who isn't Dick Greyson as Bishop, it's just Bishop being a dick. A time dick. Heroes who are hard-edged enough to kill their enemies and skilled enough to do it easily are a dime a dozen; because it violates a hard and fast rule of serials: never give your aggressive, repressed, vicariously-living readership everything they want. From the comics like this I've read, the only real plot variation you have is irrelevant personal shit that always works out in the end and determining just how evil they guy they're killing in this arc is.
To sum up, I like Batman because he is fun to read. Because his comics have to be clever. I like Batman because for every nine times his hypervigilance serves as the groundwork to defend what would be a deus ex machina win for any other character, there's a time when someone steals his files on how to kill The Justice League and everyone thinks he's a dick. I'd love to go on about how he has flaws. About how he's a dick and only begrudgingly compliments others. About how he doesn't trust anyone and won't just solve his problems once and for all. But really, all of his flaws are indeed merits nine times out of ten. I should be angry about that. I wouldn't take that crap from any other hero.
I think that one reason I can take it is because Batman has no ego (except All-Star Batman, who's cool just because he's ridiculously fun. Dude painted a whole room yellow just to fuck with Green Lantern.). Batman doesn't ask anyone to like him him. He is an island of purpose and even his peers are largely a means to an end (the better scenes that handle Wonder Woman's flirtations with him show this conflict pretty well. He does seem to feel strongly for Diana, but he doesn't want to get close because he might have to take her down one day [though eerily, as she is one of the most powerful members of the DCU who isn't vulnerable to kryptonite, it actually behooves him to get close enough to her to leverage emotional ties in the event of an eventual showdown and--oh my god, that's what he's doing with his brooding!]).
What's cool about that the thing that I said about him getting close to a female as a contingency because he has no other way to stop her is something that fits his character; he has almost no restrictions on what he'll do because he is solely devoted to his war on crime. Not because he'd form a convenient-for-him faux relationship with a woman who's a comrade in arms who's seen him through multiple threats of a global scale. His character is hard-edged without being an asshole who sees everyone solely as a potential threat.
He would do anything for crime-fighting; but he won't do that.
I think that's what resonates with fans; Batman is wholly devoted to what he does, save for his soul. His life isn't distracted or petty or irrelevant. Every moment of his waking life (and some of it sleeping and meditating) is devoted to developing ways of protecting the world and Gotham City, but as righteous as that is, as worthy as it is and as much as he ultimately gets to pursue his goals on his own terms (something that as, an aspiring writer who is very, very lazy, I consciously think about), he is ultimately beholden to his own conscience. While he could be a solitary figure of the night, prowling rooftops and hurting predators more and more each night, he finds a way to connect with others (whether its Robin or The Justice League) and reconnect with his own humanity and be encouraged to look at himself from the outside to keep his perspective.
I think is strange balance between him as a human and him as The Batman is what makes him a compelling read between arcs where he's outwitting The Joker and shooting Darkseid.
So Batman, because he's a wish-fulfillment character who has flaws I wish I had, and because he kinda has to have well-written comics.
Also, because he's a winner of cultural icon darwinism.