While Batman is the main character of both Batman: Arkham City and its predecessor Arkham Asylum, neither game lets you play his alter ego Bruce Wayne.
"Because it’s a Batman game. He’s powerful and aspirational but you never lose sight of the fact that he is mortal," Rocksteady Studios marketing manager Dax Ginn told PlayStation.Blog. "It’s such fertile ground and in Arkham City we will go deeper into the man behind the cowl by bringing in characters like Hugo Strange, who knows Batman’s true identity, and Talia al Ghul, who has a romantic relationship with him."
"Through those characters we see his vulnerable side but our aim has always been to make an action game, not a business simulator, and when you start thinking about what you would do while playing as Bruce Wayne, it doesn’t seem terribly exciting in comparison."
Arkham City's structure doesn't really lend itself to a Bruce Wayne segment, anyway. Batman is trapped inside a walled-off section of Gotham filled with the city's most vile criminals. He's pretty much in "battle mode" the whole time. There's no reason for him to remove the cowl.
Still, the idea of having to maintain a secret identity in a video game is interesting. It's not something attempted very often. Splinter Cell: Double Agent was sort of like that. The player controlled a government agent that had to infiltrate a terrorist group. He had to perform terrorist activities but limit the damage so he'd maintain the trust of his agency. In Vampire: The Masquerade - Bloodlines, players took on the role of vampires who had to fit into society by not using supernatural abilities or feeding in view of humans.
Still, I'm not sure there's ever been a game that focused on the double identity of a super hero. The Arkham series already has its niche so it probably won't go there. It seems like an opportunity for some other developer, though.