Yeah, Bruce Wayne is an eccentric rich guy in a city full of eccentric rich people up to their own shenanigans. And depending on the timeline or continuity, he doesn't even run his own company most of the time, so wouldn't necessarily be in the public eye all the time.
For Clark Kent, I've always loved the idea of certain key figures in the Daily Planet figuring it out themselves but keeping it to themselves. In the new movie, I very much got the impression that Perry White and Jimmy Olsen know. And IMO, ever since Lois figured it out herself in My Adventures with Superman, that's the way it always should be from now and the versions where Superman keeps the secret for years and years aren't the same now.
For me, the ones where it gets difficult to justify their secret identities remaining intact for long are characters like Static or Spider-Man that still go to school and live with their parents / guardians, and regularly slip away during trouble to regularly rescue their friends and family as their superhero selves.


