The second question seems a bit obtuse: are we premising that ‘society’ is the citizenry of the United States of America? And if so, that the electoral process, regardless of participating gender, somehow effectively betters the entity?
Women tend to not be competitive or find interest in conflict. Conflict can be a great way to find out what is true.
Diversity is a strength because multiple PoVs can eliminate problems that a narrow PoV could miss.
In Europe, men are significantly more inclined than women to vote right-wing, far-right & conservative parties. I would welcome a revocation of the right to vote for men (until finally there are no more fascists).
The odds ratio on the women-no-vote poll was 7.6:5.3 ~= 1.4x (men more in favor than women).
Right now the odds ratio on the men-no vote is 7.0:2.0 ~= 3.5x (women more in favor than men).
I hope this is an artifact of the voters - 30% fewer women so far.