take the word “asexual” and say “Yes asexual people still want sex!”

Yeah but nobody is doing that. More accurate would be “Asexual people might still want sex, if it’s important to you, please ask (appropriately)”.

If you want “asexual” to exclusively mean people who feel no sexual attraction and are sex-repulsed, then what would you propose people who experience no sexual attraction who are still sex-favorable or sex-neutral should call themselves? Like, I’m sympathetic to your frustration, but they also deserve a label

we’re after a way to clearly communicate no.

There is, it’s saying “I don’t want sex” or “I’m sex repulsed”. It’s even better because anyone can use that regardless of their sexual attraction, even.