You premise about patriarchy being more efficient is false. First you have to agree what constitutes "efficiency". If you used the classical description about "covering needs", then matriarchy worked better (As proven by Amartya Sen). Actual system is unsustainable since is consuming more resources than recovering rate. so even from an economic perspective, patriarchy is not more "efficient" in the long term. In fact, whenever population reach a point where there are not enough resources, it comes to a big wa that set society back several centuries. It has happened several times through history. It would happen again if we don't correct course.

By the way, wasting exceptional women is wasting resources. You don't know if the next technological breakout would have been made by a woman and you would need to wait several decades until a man does that. and that might be doing even a greater breakthrough if he can use the previous one by a women. So not efficient at all.