^Does she also throw lightning bolts and shape shift? I really wouldn't try to apply too much logic to the abilities and heredity of mythical Greek gods. Besides, didn't Hades end up in charge of the underworld by drawing lots? Commanding the dead was more of a job description than his raison d'etre.
Still, I'm no expert on comic book lore, but I was under the impression that Diana's innate abilities were about on par (give or take) with her fellow Amazons and the flying, super-strength, bullet deflecting etc. being a gift given to her after the fact (possibly tied to her armour?) I suppose it depends which version of events you subscribe to as I imagine her origin story has been re-written and re-imagined about as often as Superman's.