It seems like a pretty obvious tactical error. It'd be easy for a criminal to inflict serious damage on the area. He could get his jaw/teeth broken by a fist, baseball bat, crowbar, etc. Not to mention it gives clues to his identity - skin color, shape of mouth, dental records (if anyone can get that close to him).
really the reason is because he has always been drawn that way. If batman was real I am sure he would have a helmet of some kind.