He's virtually bald compared to what The Joker has.
http://img-www.theonering.net/staff/xoanon/TDC/paul_bettany1.jpg
compared to:
At the moment I can't think of any reason why he would need one, since they are trying to tone everything down and make it more realistic. You get a guy like Firefly who could work in these films but chances are won't be in it, but you don't need him to be in the plane, because he has his cape that can glide now. Joker and Two-Face aren't villains that would pull off aerial stunts, lol. I can't think of any reason why he would use it.