This reminds me of a short that Brian Azzarello did for "Batman: Black and White", which sort of shot down the idea that Batman maintaining the facade of an urban legend would help his own cause.
Basically, people would probably be more scared to know that there most certainly is a lunatic out there who will beat you to a pulp if you try to commit a crime,rather than hearing about a rumored bat monster.
While here Bats does say that the people who need to know he exists already do, Brian's story revolves around 2 teenagers who have just entered the trade and end up getting killed by rivals during the first days on the job.