I don't know the history of all sports, but the few tidbits I know all point to sex/gender separation as being initially based on beliefs that women were inferior to men. From physical sports to mental ones like chess, sex separation was due to women not being seen as equal to men. I think its time to do away with separations on sex, and go with ones based on ability and size. Boxing does it with weight classes, why…
I've often heard that women (in general) have ~5% more body fat percentage than males, because of how their body work. That means that if you have two 100kg people in optimal conditions, a man and a woman, the man would have on average 5kg of muscle more than the woman. This is a HUGE difference and wouldn't make for fair fights.