I'm not convinced that there still is that full sense of "freedom to choose" that you suggest. In your argument that genders naturally tend towards certain careers, how certain are you that you've eliminated systemic bias that may still cause inequalities in occupation and opportunity?
For example, I suspect a similar argument could have been made a few decades ago about why women tend to be nurses not doctors, or why women tend to teach only in elementary but not university settings.
For your argument to have full merit, you'd have to run an experiment in a truly unbiased, gender equal culture. One does not exist. Therefore, your argument rests largely on a hypothesis that, "see, this is the way things are and that says something about the innate nature of gender."
To really challenge yourself, take your comment and swap out gender for race. Would you still feel as comfortable to suggest that, "... where all races have the highest levels of equality of opportunity, education, and choice in the world...is that that racial effects are actually maximized. Whites tend to choose professional careers and competitive paths because they are free to choose, and Mexicans tend to choose to become gardeners and low wage workers of any kind, because they are also free to choose."
If that feels uncomfortable, then perhaps your premise needs reevaluated.