Even in a largely non-contact sport designed from the ground up to be mixed (i.e. there are different rules, points and even equipment for the sexes) they can never cancel out the male advantage. Women end up playing the less enjoyable positions, they still risk injury, and they will play a less significant role in the game.
This isn't borne out in my daughters experience in cricket. She opens the bowling in her men's team in the men's league and won player of the year at the awards ceremonies!
She has been promoted up through the league over time which has 8 divisions.
She is a county girls player. The best female players can compete in the highest men's leagues but would never be good enough to play for the England men's teams or top counties.
I just think that we have to be careful what we wish for. Ending participation of women in men's leagues, where they can, would be detrimental for women's sport.