'if they were going to make women's lives better. Small snag: first you have to know what a woman is'
No, you DON'T need to know what a woman is to make women's lives better (well, yes if you're a doctor, but not if you're a politician). You need to do two things: make people's lives better in general, and avoid excluding women from these benefits,
The leaders who denied women the vote at all until 1918, and on a fully equal basis until 1928, knew what a woman was, and used this knowledge to exclude women.
The leaders who denied women the right to equal pay until 1976 knew what a woman was, and used this knowledge to deprive women.
The leaders who did not make marital rape a crime in law until 1994 knew what a woman was, and used this knowledge to allow men to abuse women.
The leaders in Afghanistan who deny girls the right to an education, and women thwe right to most forms of employment, know what a woman is, and use this knowledge tooppress women.
Most leaders who support policies that keep many people in poverty know what a woman is, but at best don't mind disproprtionately harming and disadvantaging women.