Men aren't going to be on the front line of this for the same reason white people aren't on the front line of combating racism [0]: even if we don't do awful things one side effect of which is to reinforce privilege, we still benefit from that privilege. A woman seeking funding has to worry about all the things a man seeking funding has to worry about, plus she has to deal with being pressured into sex. That's not great for society, but it is an advantage for men.

[0] as a white man, it is my privilege to make sweeping statements about whites and men b^)