I think you may have misread what I was suggesting.
Trans people should never have to disclose part of their medical history to stay employed. Even if you get regular testing and it’s no big deal, what goes into your medical record should be between you, your doctor, and no one else. There should never be a scenario of “Star kicker of [team] barred from competition because her labs showed she is too masc.”
My point was not to suggest that as an option, but more that it would be a bad proposition to try to avoid the scenario where trans people would be incentivised to partially detransition (MtF) or take too many supplements (FtM) when athletic performance is directly correlated to how many androgens your body has.
I don’t know how to avoid that scenario in a capitalist system, to be honest with you.