Sure, but all that imperfect categories and blurry lines and whatnot is exactly what gender is for. The controversy section is indeed interesting but not really relevant. It’s good to use more specific terms like CAIS when appropriate, but if you want some term to refer to all such similar situations, intersex shouldn’t be used.

Sex is simple and serves an important purpose in biology. If we redefine sex into something that isn’t based around gamete size then biologists are just going to make up a new word that means what sex used to. Biology is hard and messy and discovering such a widespread rule is a major scientific win.

“Intersex” is confusing/misleading, DSD is the better term, there are male DSDs and female DSDs. Sex in humans is binary and immutable, because it’s defined by gamete size. Chromosome differences are variations within a sex.

But that’s the whole point of separating gender and sex. Don’t try to turning sex into something it’s not, focus on gender.