one of the things i like about Batman is that it's fundamentally about being orphaned, and being an orphan — how this guy stays tethered to the world in his own weird, abstract, extrajudicial way when he feels that his link to it has been violently severed

Batman does this by permanently recapitulating his own trauma: solving crimes for other people, protecting them. But that's actually just the beginning; he also recapitulates his own experience of orphanness by essentially raising several orphans

Dick is an orphan in the traditional sense: dead parents. Batman sees it happen. Jason, less so: missing dad, known mom who eventually dies. Tim, even less so: parents are around a while, and involved, before both dying. Carrie, even less than that: negligent parents.

Steph: evil father, who openly works against her. And then there's Damian, whose parents are both alive and yet both have identities that totally obliterate their role as his parents. He doesn't relate to them as a mother and father; he can't, and neither can they.

In all these different cases, Batman tries all these different ways of making orphanness for them not what it was for him: Either by trying to teach them the (arguably poor) coping skills early that he learned over a very long time, or by literally legally adopting them, etc.