I think the reason why "baby" bugged so many people before is that it's not something most versions of Batman would say. Batman generally tends not to use that much slang, and sometimes speaks quite formally, I find.
What's interesting is that most versions of Batman have him too emotionally crippled for him to even use terms of endearment (y'know, beyond calling Robin "old chum").
But this is ASBAR, and the Goddamn Batman proved he is beyond predictable speech patterns in this universe!