“men CAN, but women MUST–the way that men must do those other things, and women can, but don’t necessarily have to”
Actually, that is incorrect. Not all Jewish men know this, but if they don’t have a woman lighting Shabat candles for them they must light themselves. If a woman OR a man bakes a sufficiently large amount of bread (CYLOR for the exact amount), no Jew can eat it until challah is taken whether the baker is a man or a woman. And of course both women and men must follow taharat hamishpachah.