Its a symbolic costume for sure... But if we're going to quote BB, remember they played up Thomas Wayne's charitable deeds as equally symbolic. Wayne Tower was to be a symbolic beacon, as was the mass-transit system. In a corrupt city, you could argue that somebody high up who actually cares and is dedicated to cleaning up the town and helping the little guys (Harvey Dent and Jim Gordon as well), has a stronger symbolic power than stopping the occasional crime and nobody really knowing about it except the one victim you saved, the one witness, and the one desperate criminal you hospitalised. The Batman outfit wasn't the only symbolic act open to him (given he could have continued in his father's footsteps), but it WAS the most personally satisfying choice since it means he can enact revenge on similar desperate people who robbed him of his parents and childhood.
As for being a symbol of hope, he hasn't quite picked the correct costume to do it. Superman's outfit is a symbol of hope, Batman's outfit is a symbol of fear (DESIGNED to create fear). The distinction between those who have to fear him (criminals) and those who don't (anybody else) isn't quite clear... Nobody ever seems to trust him at first, certainly not the police force or newspapers. If he's on OUR side, what has he got to hide? (Superman at least gives us a smile and a wink).
Bruce dedicates only a small fraction of his day to his charitable deeds, and he's hardly obsessed about it in the same way he's obsessed about perfecting his physique and crime-fighting skills. Half the time he's written as a spoilt jet-setting fop to keep from drawing the wrong type of attention to himself. He might sneak in a charitable deed here or there, but no more than the above average socialite who wants to feel good about themselves, and certainly not at the level of his father.
Goyer/Nolan correctly wrote Bruce this way in Batman Begins, but they also made pains to identify that his mission is very much at its core one about personal retribution, not some greater sense of civic responsibility. If it was civic responsibility with no personal motive, he'd do as his father did. But since his primary drive is a revenge which can never be fulfilled, he's attempting to find a middleground which meets his need for personal retribution/empowerment, as well as (kinda-sorta) following in his father's footsteps as symbolic beacon of hope for Gotham.
Spiderman doesn't leap around and stop crime to avenge his uncle, he leaps around because he knows that with his power comes a responsibility to help others because he has the unique power to do so. Batman HAS the unique power (money) but he's not using it. He's saving it to keep from drawing attention to himself, he's spending it on a new wing or a bigger plasma screen for the batcave (honestly, how big does the bat computer's screen have to be? all he does is project enormous photos of the villains on it and brood anyway).
If he wasn't about personal empowerment, he'd keep Gordon in the loop during his investigations, he'd allow the police use of some his vast lab/computer/oracle crime-fighting resources (he occasionally does, but its the exception rather than the rule)... he needs to feel indespensible in the ground-level fight against crime... If he really cared only for the city, he never would have left to brood over his own personal tragedy.