I do agree that disguise is one reason. But this is Nolan, there's always more. In Batman Begins, Bruce tells Alfred:
Bruce Wayne: People need dramatic examples to shake them out of apathy
and I can't do that as Bruce Wayne, as a man I'm flesh and blood I can
be ignored I can be destroyed but as a symbol, as a symbol I can be
incorruptible, I can be everlasting.
Alfred Pennyworth: What symbol?
Bruce Wayne: Something elemental, something terrifying.
Though, the consequent scenes do not talk much about the symbol part and everybody pretty much forgets Bruce's original idea of Batman. We start thinking of Batman as Bruce with a costume on and fighting the bad guys. Which is true but to Bruce it's something more, like he says to Alfred. It's a symbol to terrify people.
If you were a villain it wouldn't be easy for you to think that Batman is just a guy with a mask on. That makes it more terrifying. The idea of someone powerful than the ordinary human. And Bruce takes every possibility to make the idea a very real and unshakable threat to the bad guys.
The voice, the bat ears, the dramatic entrances and exits - all these are trivial to the plot. Either way it's not going to change the output of a scene if Batman enters sneakily with a very chilly line or just through the door. But Bruce takes the extra step to go through all the mumbo-jumbo just to keep the idea real. The idea of a legend. The idea of a permanent warrior who is going to fight the bad guys every turn and forever.
It all makes sense. Come to think of it. Joker says something similar to:
"You'll be outcast too. They'll see you as a freak when they are done."
Joker is a schizophrenic villain who wears face paint all day long and he empathizes with Bruce. He actually identifies himself with Batman. You can understand the similarities - Bruce goes to great extents to protect the man behind the mask. Same thing goes for Joker - he wears face paint 24x7. Without it, he wouldn't be as scary. And scary is important to him.
Bruce takes the idea of Batman more seriously than the audience are led to believe. The outcome of it is one thing - crimefighting. He does take that seriously. But he also takes the very idea of Batman personally and he is proud of it.