>What differences in social roles have been proven "necessary"?

Given that we're in a huge democraphic crisis which will bring untold disaster and misery, a huge depression crisis, marriage crises, and a loneliness epidemic, perhaps we're not the best arbiters of whether they've been proven "necessary" or not.

As for the questions, to some degree they indeed do, so partly yes, but also those differences in treatment are not on a case by case basis, but on average.