The most recent Batman comic collection had a really interesting story.
In the current continuity Batman and Catwoman are about to be married. Booster Gold (a time traveling superhero who is often kind of a screw up) is inspired by what happened to Superman in the famous story “For the Man Who Has Everything” to, as a wedding gift, go back in time and save Bruce Wayne’s parents. His idea is to show him that reality would actually be pretty awful so he would appreciate his current reality. Yes, that is a dumb idea but he is Booster Gold and doesn’t often think things through.
So we get to see what the world is like without a Batman, or at least without Bruce Wayne as Batman and it is just as bad as you would expect it to be. If you enjoy Batman stories I would suggest checking it out.
No, not at all. The current Batwoman’s premise is that she was a soldier who was washed out of the military under “Don’t Ask, Don’t Tell” when someone anonymously informed her commander she was a lesbian. She’s aimless and a little self destructive for a couple months, until one night some guy tries to mug her. She beats the crap out of him, and Batman shows up right at the end. Although she doesn’t need his help, she realizes that she can follow his example and help others, and starts dressing as Batwoman.
The previous incarnation of the character, introduced in the '50s as a response to hysteria around comic books being an immoral influence on children, was created specifically to give Batman a romantic interest, and defuse speculation that Batman and Robin were gay. I’m not particularly familiar with any of her stories, but the whole, “Exists to be Batman’s beard,” sort of requires that Batman still be around for those stories.
‘Batman being gone’ is the premise that leads to the creation of…
Batman.
Specifically the Jean-Paul Valley version who would become Azrael, the Dick Grayson version, and the Jim Gordon power-suited official police version.
Dick and Jim would both give Bruce the identity back, and Jean-Paul have it taken away for being…a bit excessive in his methods.
There was also Harvey Dent’s brief time as a hero, at Batman’s request. (That ended badly when he was falsely accused of some murders and the anger made the Two-Face persona return.)
Note, all of these are replacements - inspired, or actually requested, by Batman, when he’s taken out of the picture for various reasons. (Injury, apparent death (time travel), apparent death (amnesia), and training.)
Versions of Gotham where there never was a Batman are either dystopian (as in The Gift), as nobody rose up to fight the corruption, or utopian so Batman was never needed in the first place. (I can’t think of an example of the latter, but I know I’ve seen it.)
There’s also that alternate timeline (Dammit, Barry!) where a young Bruce Wayne is killed in an ally by a mugger, inspiring Thomas Wayne to become Batman - and Martha Wayne to become the Joker.
