The most interesting thing about Damian Wayne is that he is a bird.
Damian, unlike a lot of the batfam, doesn't hold that deep connection to gotham that the other robins and batgirls do. He views Gotham in an intrinsically different to the way Bruce views gotham. He never grew up there, he immigrated to America after years of training under the league of assassins.
Of course, he still cares about Gotham, but the difference between him and the others is that he views "the mission" in a fundamentally different way.
The mission, to Damian, includes travelling the world to return artifacts he stole as a child.
The mission, to Damian, means granting failed clone attempts of himself asylum through an island he owned and giving them peace.
His mission is granting a girl who he killed the father of a home where she's being served and given the peace she was never given as a child.
His mission is taking in animals, no matter the species, because everything matters.
The mission, to Damian, includes travelling to another part of the country and kidnapping a team of people to inform them they're being hunted done by the LoA.
The mission, to Damian, means fighting in a death tournament near Argentina because he smelt something suspicious.
More than half of Damians runs take place outside of Gotham. RSoB, Teen titans, Super sons (all 3 of em), robin 2021. His mission will never be tied to Gotham. He protects Gotham, he works under Batman, but it's never an odd day when Damian leaves and does something on his own without permission.