I think its one of those things for when you want a character good at melee combat, any kind of combat. Sure the Hulk gets by with a huge strength and ranks in Close Combat: Unarmed, and presumably so can Batman. But for a character like say Lady Shiva you want a character that if they're given a sword they can fight, if they're unarmed they can fight, if they have alien bluntonium energy doohickeys they can fight. So fighting as an ability make sense in a obtuse sort of way. Also, if you drop Fighting and Dexterity we're back to 2E M&M with the classic six attributes, and raising attack bonus and defenses directly via points.