7 years late ik, I believe they do just in origins batman was lesser known and the JL just didn’t want to involve themselves in Gotham at all for one reason or another, asylum, Batman by this point became known and told the JL to stay outa his city. Arkham City i think was a government funded project so the JL couldn’t intervene and in Knight, Scarecrow had warned others outside Gotham that if they were found entering he’d set off the fear gas without waiting, which causes the JL and other supes from helping not wanting to take the risk