At this point in time, we need to talk about adding "sex" rather than adding "gender" because most Americans live in states where the two categories have already been mashed together into a single (useless) one which suffers all the deficiencies you mentioned above but also fails to tell us sex at birth.
Fair enough, and I do think that having separate listings for sex and gender is a better solution than having one called sex which is just a gender self-ID in practice.