That's a dumb comparison. The reason women have their own categories is not that they psychologically feel they're women and don't want to compete with people who psychologically feel they're men - it's because they can't compete biologically, so such categories should be based on biological considerations. If it was mixed, men would dominate all sports - that's the reason there is women's sports in the first place. Introduce man -> woman transgender athletes and these women now can't compete in their own category either, so they have nowhere where they can compete on equal ground.
It's in no way comparable to what is merely a superior training system. USA puts significant funding into their system, and other countries are free to fund their own systems as well.