Women and men are both equally chayiv in kiddush, at least on shabbos. Additionally there is a commonly known rule that a non obligated person (or obligated on a lower level) cannot fulfill a mitzvah on behalf of somone who is obligated. I’ve heard it said in the name of Rabbi Akiva Eger that men can make kiddush for women even after davening (and becoming only rabbinicly obligated) because in fact they're still obligated מדאורייתא because they intended not to "give up" their obligation.
But what about on Shabbos day, where they actually make kiddush in shul then go home? Then they aren't obligated anymore because they DID intend to get rid of their obligation and the women are still obligated rabbinically (it's day so it's not מדאורייתא).
So why the common Minhag for men is to eat kiddush at shul and still make kiddush for their family's at home?