Would the world be better if we didn’t recognize genders?

In such a world, there would be males and females, but nothing associated with what it means to be male or female other than biological facts. Men and women would be equally likely to be social leaders. And there would be no stereotypically male or female behavior.

In this world, there’d be true sex equality, and, it seems, no need for trans activists. Should we fight for such a world?