This is like saying "yes, gay men can still have sex with women, as long as they're not attracted to them. They're still gay! It's only a name!"
Well... That's correct, though. It might be a little easier to see if you consider the stereotype of male-on-male sex in prisons or militaries. Or, to keep closer to your example, a homosexual man having sex with a woman just to see what it's like. Or because he's closeted and trying to conform to social pressure. There are lots of reasons to have sex with someone, and having sex with people of a particular gender does not necessarily determine your sexuality, if sexual attraction is not one of them. I mean, sure, a gay man having sex with lots of women for apparently no other reason than that he likes it might be a little sus, but, like, you might just not know what's going on.
The amount of times I've been asked if I'm "one of those asexuals who have sex" is gross.
I agree that that's gross. But not because it implies that it's valid for asexuals to like sex. It's gross because that is a weirdly intimate detail to just ask casually about, regardless of your sexuality.
because it apparently includes everybody.
No. Only those who don't feel sexual attraction towards others. Regardless of whether they like having sex or not.
I am against not being able to use the label to distinguish clear what I identify as anymore
If the "not having sex" part is important to you, what's wrong with identifying as "sex-repulsed asexual" instead of just "asexual"? Sounds like that would already solve your problem
I mean... It might be. Just depends on how much potential there still is to get models up to higher reasoning capabilities, and I don't think anyone really knows that yet