Why should sports continue to separate players by sex (or gender) classes rather than simply use ability-based classes?

Sports currently tend to use sex classes to separate players, before further ranking into classes based on ability or weight ranges. I assume this is a global norm, and it is certainly the case in all well-known sport competitions I've seen and in major international events such as the Olympic Games, where events are labelled 'mens' or 'womens', with some recent addition of 'mixed-gender' team/relay events, which is basically equal men and women, usually competing independently rather than different sexes competing. Mixed doubles tennis is a possible rare exception.

This topic asks if this model of separating sports players into physical sex categories (or social gender categories) is appropriate, or if both sexes should be in the same leagues.

Potential starting arguments:

For:

• Having men dominate most sports where athleticism or muscle strength is a major factor would be demotivating for women. Top leagues (that get televised) may just become entirely men, with no women's league.
• Furthermore, competitions with prize money for winning would generally be very strongly biased against one of the sexes with an inherent physical disadvantage
• Heteronormative society makes mixed-sex groups more prone to sexual harassment, compounded by the energetic nature of sport

Against:

• Sex is a just a crude approximation of strength or ability, which is its own category/grading in most competitions.
• Intersex people (that is, who have chromosomes or sex organs which do not fit standard male or female) complicate this system. This page lists some examples Olympic intersex athletes competing in or disqualified from female events.

Compromise:

• The arguments for men dominating top leagues is irrelevant for non-professional sport leagues such as local competitions, where sport is aimed at fun and social interaction, which should not needlessly encourage sex segregation.

NOTE: This debate topic is not about 'trans in sport' issues. While that topic is linked, because removing sex/gender classes would make that issue obsolete, that debate in itself shouldn't be held in this post.