What you're describing would very, very quickly end up with essentially what we have now - mens and womens sports. The men would be in all the top ones, and the women would all be in the bottom ones, with the trans women at the top of the womens ones at the lowest, with many much higher since they have the physical ability to compete with men.
Did you know that there is no rule stating that all NBA players have to be male? Same with the NFL. Same with the NHL. Same with almost every professional sporting competition in the world that is thought to be a "male" competition. When you understand why you've never seen a single female compete in any of those competitions, and notice that some of those have their own separate "female only" competitions, maybe you'll have a lightbulb moment.
Wow good one sherlock! Just like 99.9% of the worlds population, yes, my "gender identity" is the same as my sex. Well it would be if I had a "gender identity".