I think you mean sports without a physical activity aspect; and even then, sports like chess don’t separate males and females (they offer female-only competitions).
There’s no other point to segregating sports by gender, just straight white cis dudes getting bent out of shape by any challenge to their supposed superiority.
What are you on about? There are two HUGE reasons: safety and fairness:
Especially in contact sports, allowing women to play with men is not safe, and would only lead to an environment conducive to women getting injured.
There would be zero professional female athletes (excluding sports that only require mental strategy ofc) if there were no separate leagues for women. They wouldn’t perform at even close to the same level as the men, AND would be at increased risk of injury.
I don’t know what fantasy world you live in, but here are biological factors that make it necessary to separate men and women in order to have fair competition. Female athletes would be infinitely worse off if forced to try to compete in a single league shared with men, because they aren’t be able to.