I'm not a fan either. But the way to justify it would be for Bruce to decide he wants to groom a successor, should anything happen to him, because that's how important Batman to Gotham.
If it's done-
Dick Grayson shouldn't be someone out on every patrol. Bruce calls him in infrequently, to give him experience.
And I would be interested to see how Nolan would re-design his look. No flimsy brights colours, but armoured protection, complete with helmet and mask/goggles I'll bet.
Maybe he would announce his presence differently, with a piercing bird shriek (recorded) to freak out bad guys, which is the opposite of Batman because he approaches silently. Just ideas off the top of my head.