With such a small subset of the population, statistically there wouldn't be an even mix. But IMO there should be at least some representation of every "protected" attribute. There's plenty of women with the physique and skills to fill roles in the NFL, for example. Not every player needs to be able to be a linebacker, after all.
Please provide three examples. I played college football at a tiny division 2 school and have never met a woman (I live in the gym these days) for which this is close to true.
Even if you're referring to a low/no contact position like kicker/punter you're still under threat of a 220 lb linebacker destroying you [1].
Doubt it, outside of possibly kicker. Otherwise, you wouldn't see the biological differences in track and field performances between males and females, given how much football relies on physical attributes like size, strength and explosiveness.
There could be a professional female league of course, like the WNBA for basketball. But if even tennis has to keep men and women separate to be fair, then there's little chance a physical sport like the NFL would be competitive for women alongside men.
I will grant you this. A top-level woman can not out-physical a top-level man.
But, there's more to professional sports than just physicality. You brought up Tennis - but as proven in the various exhibition matches, women have not been cleanly swept as one might expect, and many have won over the years.
This leads me to say that there's room even in the physically intensive sports for both genders, not to mention in the less physically intensive sports.
https://en.wikipedia.org/wiki/Battle_of_the_Sexes_%28tennis%...
I say complicated because it's not just about the number of people employed, but also how much they're paid, whether or not there are separate leagues, what about the coaching staff, etc.
It's fine to think of pro sports as one of the very few professions where you're performing so close to the human limit that biology actually becomes a factor. It's not just gender, for example short people won't be equally represented in many sports, which does not need to be true for almost any other job.