As far as this idea about asexuals having sex and even wanting it in some sense, I suspect part of it is the people who talk about these divisions have a very narrow idea about what sexual desire is meant to look like.
This is why they claim that "demisexual" is a sexuality - the idea that someone might want sex only with feelings of attachment is seen as somehow different than just a normal personality thing that might even be just for a period in life.
Similarly, my friend's dickhead husband recently "came out" to he as polysexual, which is to say, he'd like to shag other women.
Realistically, the idea that people will only have sex for reasons of sexual desire, or lust, or whatever you want to call it, is unrealistic. There are lots of valid reasons for people to have sex. Getting pregnant being the most obvious, but also a desire for intimacy, or because they are marries/in a relationship they value with someone who would like to have sex, etc. There is a big difference between not being super sexually motivated and actively not wanting sex in terms of how someone might make decisions about relationships.
It used to be that adults were considered capable of making decisions based on their long and short term feelings and commitments about all of this, and didn't have to label it. Now they do seem to want those labels, but since there are millions of people with different circumstances and goals, it's pretty impossible.