Rather than try to create some plausible reason why Bruce Wayne wouldn't be, not just considered a possibility, but one of the highest candidates on the list of Batman suspects (frankly there isn't one), I just consider it one of the suspensions of disbelief required for the Batman story to be possible at all - along with Batman (and some others) being able to defeat dozens of people in hand to hand combat, his feats of stealth, the existence of some of the technology, the idea of the League Of Shadows existing, the Joker being able to operate for so long without being caught, the affinity of villainous people to use masks, make up and pseudonyms, etc. Sure, all of them have some in-universe justification (he was trained by the League Of Shadows, etc.) but I think really they're just unrealistic things you have to accept as being somehow realistic in this universe - the Nolan films cut out a lot more things like that than you find in most comic book films, but you can't get rid of all of them if you want to keep the story even remotely like Batman.
So yeah, I just assume that even though in the real world Batman's identity would be quickly put together by his legions of fans on the internet (look at how popular superheroes are and imagine how many fanboys one would have in real life), for some reason it just doesn't happen in the Batman universe - the people of Gotham aren't just idiots, it's just difficult to make the connection that Bruce Wayne is potentially Batman, even though it appears like it would be easy in real life. That's why I really didn't like when Robin just knows Bruce Wayne is Batman from the look on his face. Yes, it is an easy connection to make. But having someone make that connection so easily, rather than making it more believable, only serves to break the suspension of disbelief that's been required so far. It'd be like watching Batman defeat dozens of enemies with his martial arts over the course of the three films, then at the end pointing out how unrealistic it is and having a few henchman gang up and get the better of him because no matter who you've been trained by, beating multiple opponents can be near impossible. It'djust highlight that all the fights you've seen up until now have been completely fictional, or suggest that all the enemies he faced before were ridiculously poor fighters.
Well, that's my reasoning for why Robin knowing without a satisfactoy explanation is a flaw with the film - it's not like it ruined the movie or anything like that. But it's one thing about the Robin storyline I don't like.