Rationally, he understands that saving a kid from a mugger can't take precedence over saving the city or the world (besides, the kid will be just as dead if the world's destroyed).
Emotionally, every large-scale threat he has to stop or help stop, every personal enemy attacking him he has to defend from, is time away from doing his real job. I bet he behaves cold and distant even from most non-Gotham allies because he's internally screaming at them "Stop bothering me and. Do. Your. Fucking. Job." but he can't because he doesn't trust that they will.
Bottom line, we seldom (and every reboot, it seems, less often) see Batman "doing Batman." We see Batman distracted from his work by the crazy and the less-competent-than-they-should-be, and you know how absolutely frustrating and soul-destroying it is to have to constantly take time away from meaningful work because others failing at theirs. He'd probably be much less grumpy if he could dedicate himself fully to city-level crime and corruption.
As it is, he has to do that, and Rogues stuff, and JLA stuff, and he can't, and he has to put the important things last, and gods, I'm getting stressed myself just imagining it.