Women would be crushed. As far as physical sports at the highest levels of play are concerned, women are inferior to men. That's not to say that women are lesser because of it, but that's just how it goes.

Karsten Braasch (peaked out at around 40th worldwide) beat both of the Williams sisters (both rank 1 players) back-to-back. He was twice their age and known for smoking cigarettes during changeovers. Male weightlifting records are hundreds of pounds higher than women's records. There are thousands of male sprinters who have posted a better time than the _world record_ female sprinter. I don't think there's even any data to compare men vs. women in combat sports like boxing because anybody who has ever paid any attention to sports can tell you it's an awful idea.

Yeah, we could do away with the separations, as long as you can accept that women will almost always take the back-seat at high levels of play.