Re: Why does Batman leave his mouth exposed?
Having Batman's face exposed is possibly similar to why to he has a cape, at least in comic terms. A cape helped give the character a sense of motion within the static images of the comics' medium. Of course, his image was also inspired by the fact that the film Zorro had a cape. Having the lower part of his face exposed also allows the character to show expression which would be really hard or very limited to do if all you had were the eye slits visible. And again Zorro had his lower face exposed as well.
STAR TREK: 1964-1991, 2013-?