Also, imagine how awkward it is to be the determining doc in that situation.

Sex isn’t directly determined by chromosomes, it is determined by someone taking a look at the sex organs. This works for most people, but embryonic development is like most things complicated and there are a lot of factors that make it more difficult than “male” and “female”. Examples are people with more than 2 chromosomes or that have absorbed a sibling in the womb. Difference of sex development is estimated to affect 1/100 people.

So when the doc takes a look just before 6 weeks, she must declare “the embryo has ovaries and no testes - female” at every single person. At literal conception: “Idk know, man, it is just 1 cell”.