I am, oddly, going to blame traditional philosophers for this one. Our excess focus on definitions as defining a set down to every element has produced only a lot of problems when it comes to conventional language (or even precise scientific language).

If philosophers of language and of knowledge had gotten more comfortable with the idea of definition-by-archetype, at least the confirmation hearing questions would be more interesting.

So I agree (I think) with you: The definition of "woman" is centered on the typical phenotypes displayed by adult humans with female (XX) genotype. That is, a "woman" is typically someone who is meaningfully more "like that" than whatever else we might consider which we're trying to narrow down by saying "woman".

Then we can get back to talking about something that actually deserves some thought, whether it be the precise boundaries of how we want to use the word (not the core definition), or about all the unusual stuff that can happen biologically to result in less common genotypes and phenotypes, and/or about interpretations of case law, as appropriate.