It means you don't have to deal with as much social and sexual drama between team members for team sports, which I suspect (but don't have data because I don't think adequate studies have been done) distracts from practicing the sport. This is a similar problem to mixed-sex infantry squads. You can wish for all the equality you want, but you won't get it.
It means you have many varieties of sports with women competing that girls and other women can look up to as role models or inspiration or motivation to participate in sports.
There may be a good reason to segregate some sports by some traits linked to sex (but “genitals at birth” probably isn't the best standard for that), but even if there is it doesn't require immutable legal gender to do that.
If the government's standards aren't good, and are in fact simply "genitals at birth", then that needs to be fixed, but as far as I can tell that's not true, at least federally or for the state I checked. If you transition, you get a court document with a doctor's statement certifying it, and you update your gender on your official documents. Right? There probably need to be different legal standards based on the purpose the gender is being used for, too. Being a trans woman shouldn't allow you to compete in women's MMA, for instance; there's already been an instance of that happening and it was a disaster.
What concrete problem or injustice are you trying to correct? That people can't decide to change genders for a day, or decide they want to be officially recognized as the opposite gender before they transition? Is that a problem?
People seem to want [biological] sex labels to mirror how they present themselves to others, instead of mirroring (as closely as possible, based on the reason the gender label is being requested) the underlying sex characteristic / hormonal physical reality of their body. That strikes me as a problem. In the limited situations and cases where people are asking for [biological] gender and need to know, how you present yourself ceases to matter. If they don't need to know, they you can use whatever label you want. Same with your name, or your date of birth, or anything else. But it's almost always pointless to informally declare your gender, because anyone interacting with you is going to pick up on what gender you present yourself as (whether verbally, in temperament, or physically). Labelling yourself other than your biological gender isn't needed for enlightened, tolerant people, and will only antagonize people who aren't comfortable with the whole trans/non-binary thing.
> It gets women in the Olympics.
No, it doesn't. Even to the extent segregation on a fixed biological definition of sex might do that, the IOC can (and does!) regulate standards for that gender segregation (and keeps tweaking details of the rules, which aren't based on fixed-at-birth sex), it isn't constrained to using legal gender as the basis. So fixing legal gender around some biological traits at birth doesn't get you anything in that regard. Which should be obvious, even aside form knowing the Olympic rules, just from the fact that many participating nations (including the current US) don't have immutably fixed-at-birth biologically-based legal gender, and are well represented by women in the Olympics.
Most sport, at any serious level, exclude the vast majority of people regardless of gender, gender identity, or biological sex, and sports with a significant sex-associated performance difference offer substantially fewer and poorer paying opportunities for the lower-performing sex whether or not they are sex-segregated.
What does fixed legal gender buy you there?