As for me, I personally went for Damian – I think of the character’s he’s not only the one most qualified, but the one who would want to honor the mantle the most.
That said, I can still see some of the other characters being around – Nightwing being around as the aged mentor, Cass running around either as Batwoman or maybe a more good guy version of Lady Shiva. I dig the idea shown in Batman #700 of Damian being the one who trains Terry McGuinness to be Batman Beyond.
I can see it as an elegant solution to how Bruce would always be Batman generation after generation, but I don’t think it’s anything more than a whimsical idea Bruce had in his head. In the end he would trust his family to keep the mission alive.
The Damian of that time definitely would, but I don’t think the Damian we’ve seen in stories after that run would.
Now that’s something I really can’t argue with. The Bat family as a whole is enough of an assurance for Bruce that the world (or at least Gotham) will be in good hands long after he’s gone. That said, I still don’t think any one member of the family could completely substitute Bruce Wayne as Batman, and I don’t feel like any of them would explicitly want to either.
Damian would be my second choice after Cass. I also thought about a Damian & Cass duo as Batman as Batwoman but the more I thought about it it didn’t make sense to me. Batwoman is Kate’s legacy to give away and, correct me if I’m wrong, but I’m pretty sure Cass and Kate don’t have the best relationship. But honestly I would dig any version of Damian and Cass working together