To be more precise there is the fallback of competing in the women only events if they get knocked out of the male competitions, snooker for example has a womens world champion who has won the title 12 years in a row but hasn't made an impact at all in the mens game, same for darts really. If we remove the female versions of sports and just allow all people regardless of gender to compete against each other they we are left with men winning most if not everything in sight.
If we genuinely want to see sport mixed and for that mixing to herald in a new meritocracy then we have to just have a world championship of any sport and none that only one sex can enter in to.