Why are we doing separate competitions for men and women? Because men have physical differences that give them a significant advantage on many sports. For simplicity purpose I will assume this is only because they generate more testosterone though I'm sure it's more complicated.
So people generating more testosterone have a significant advantage on sports. Why should then we care wether they are men or women, whatever that means? A good illustration of this are women who have hyperandrogenism, who are, ironically, sometimes excluded from competing in women competitions because of the unfair advance their high testosterone give them compared to other women, even though they are biological women. I'm sure some men have low level of testosterone compared to the "standard" level of most men, which would give them an unfair disadvantage in men competitions.
So my question is, why, rather than doing men/women competitions, don't we do high/low testosterone competition, regardless of the gender?