Anyway, as a control freak who doesn’t like or trust anyone, this makes perfect sense for Lex Luthor, and it gives you a pretty good idea about who he is. It even fits with one of his older origin stories where there’s a lab accident that causes his hair to fall out and he blames Superboy, who (if I remember correctly) saves him from his own accident (paging Doctor Doom).
That said, Batman is virtually a man without fear (with better vision, a better tailor, slightly less demon possession, a kid, a butler, fewer headstones with his name on them, three adopted kids, only one of which kind of wants to kill him, and he doesn’t live in New York either [I’d bring up that he was never played by Ben Affleck, but then…Clooney.]). He takes risks to make things better, but hope is a fundamental principle for Batman and as much as he benefits from the status quo, he would change it if it meant a better world.
I’m trying to picture a Lex/Batman dynamic that wouldn't double as a condescending amusement/nine-second takedown team-up as well. I’m sure it’s been done and it was more interesting than that (Yeah, “Kingdom Come,” where Batman Lex Luthors Lex Luthor’s antagonist role in the massive crossover story.).
Moving on to, or, well, back to pettiness. Heroes aren’t petty. Whenever I type that, it seems like a tautology. It’s almost written into the definition of hero that there is simply no room for pettiness. Batman definitely works hard to make sure that his battles with his villains aren’t personal. In part, it’s so as not to feed their egos, and consequently their bizarre psychologies, but it’s also because what he does is rarely personal. Likewise with Superman. They solve problems, not people. Maybe that’s another reason they don’t kill, hating the sin and not the sinner. There are few enough absolutely evil people in this world that there really isn’t any need to hate most of them, even when you work (well, volunteer extensively) in law enforcement. I think it’s also the type of people they are. Superman, Spider-Man, and Batman do what they do out of a desire to protect people.
Until he returned to crime, Rhino and Spider-Man would have a chat every so often. In fact, Spider-Man is currently pretty chummy with a lot of his classic rogues. If you know me personally, I’ve probably mentioned “Small Wake for a Tall Man,” where a bar full of classic Spidey villains get together for the wake of Stilt Man, who’s respectfully laid out on a pool table after Punisher shoots him during Civil War. Yes, I'm going to go over it again. In it, Spider-Man shows up to see the mourners drunk and fighting amongst themselves. He gives them a severe tongue lashing, pays his respects, and leaves. Afterwards, they feel crappy, not just for being jerks at a wake, but for getting yelled at by their archnemesis. It’s just after some of them decide to teach Spider-Man a lesson that they realize that the entire wake is a setup, The Punisher locks the place down, and it burns to the ground. While it wasn’t a Spider-Man book, it does serve as an example of how Spider-Man not only cares about his villains as people, but commands some respect from them for caring. That Spider-Man, who pays the heaviest price for being a hero (at least amongst the heroes I’ve mentioned), can care about those guys when they’ve trashed his social life and his body on multiple occasions says a lot about the guy.