a. Well, as the Algerian boxer showed, one issue is that it is unclear what constitutes "biological sex". Admittedly, it affects only a very small percentage of people, but it would seem that the logical question, at least when it comes to sports, is whether the individual has gone through male puberty, not chromosome (since note there are more possible combinations than just xx and xy and that doesn't address some rare hormonal issues). Admittedly, a small percentage of people, though I think if we did rigorous screenings on all female athletes starting at the youth level people would realize that the problem is not as rare as they thought. But admitted, it is still a small problem, so set that aside for now.
2. Fairness, as I've pointed out as a construct. Yes, a level playing field (the the extent we can get it) is a concern in sports but there are other concerns including efficiency (or we'd screen every teenager in youth soccer for PEDs) and participation (or women's sports would not exist). Fairness are the words a child uses to complain about things, and in sports things are largely determined by accidents of birth and a function of the applicable rules.
3. Given participation is a concern, it is not sufficiency to say "cisgender women only compete with cisgender women period." (BTW, nice double entendre). You also have to answer the question well how are you "fair" from a participation point of view to the people you exclude. It's not enough to say "too bad so sad, go compete with the men" (which, because testosterone suppressors and female hormones are performance reducing substances, they won't be able to do). The burden shifts to you to come up with a reasonable solution that answers the participation concern.
4. And no "just play coed" is not a sufficient answer because we don't do that with women so you have an equal protection/opportunity issue there to. We could tell women "just play coed" and do away with women's sports as well, and give that money to the "best" athletes (with the exception of some of the grace sports like iceskating and rhythmic gymnastics, are all male).