I think the ideal relationship between Batman and the Joker is incredibly lopsided. The Joker should care much more about their dynamic than Batman.
 they aren’t perfect opposites. They aren’t each other’s arch enemies. But joker NEEDS to think that.
Without Batman, the Joker is nothing. He’s just another psychopathic serial killer with a gimmick. A gimmick that doesn’t even make sense without the stoic, humorless detective hunting him.
But THE Batman has plenty of other things to do, plenty of more complicated and heartbreaking villains to oppose. Gotham is a mess and there’s always work to be done.
If the Joker were to die Batman would grieve him, yes. But not because he is missing his other half. Batman would greave him as a victim he couldn’t save.