Main problem is the fact that sports are separated by sex. Take out the transgender athletes and you still have a sexist system.
Though, I would have to say, eliminating the barriers does not exactly mean women will go into more diverse sports. Chances are, women excel and are interested in different things than men. Goes with many things and not just sports (like jobs).
Anyway, yeah- sports should be based on capacity and not sex. There's a reason we have the Paralympics, right?