If men really decided to give it 100% to competing with women, then women, on average, would be left safely in the dust. It is true that men feel that in so doing, they would be “beating up a girl.” But feminism has been around for a long time. People, men and women, don’t take kindly to being duped, including guilted into making unwarranted sacrifices. This solicitude will end, if it has not ended already, replaced (reasonably enough) with jaded cynicism. Men’s natural desire to protect women will wither, and women will be left on their own facing a hostile and defiant world. And in that case, they will be very unhappy.
Here is another way in which women’s power games are anti-social. For other women may well have to face a fire that incompetent female firefighters will fail to put out, losing their home in the process. A woman as a producer may benefit from foolish privileges to herself, but as as a consumer and citizen she does not benefit from similar privileges to other women.