There are a lot of fictional characters who, with a few small tweaks, could have been realistically portrayed as asexual. One example is Trey, one of the men of "Sex and the City". I recently re-watched the episode where Trey and Charlotte, his wife, are given homework by a sex therapist. Trey refuses to tell Charlotte about his sexual fantasies and huffs about not being "a sexual person". When Charlotte tells him that she is, indeed, sexual, he makes no move to agree that he is as well. (Most people consider it a big insult to be told they're not sexual-- if Trey saw himself as sexual, it would have made sense for him to protest Charlotte's statement.) But despite all this, he is obviously intended to be a sexual person, just an uptight one with issues.
But even if a character is intended to be asexual, how would anyone ever know? Wouldn't they be read as an uptight sexual with issues, even if their asexuality is intended? I can understand why writers would not want to use a still-unusual word like "asexual", and I know this from personal experience. I once took a writing class in which I presented a play I'd written about a woman with Asperger's syndrome. There was intense debate in the class over whether I should actually use the word "Asperger's" in the play or not. And once the word "Asperger's" was brought up, it was all anyone was willing to talk about. Other writers got to talk about character development, plot, arc, and all that other stuff-- but I only got to talk about Asperger's. It was extremely frustrating. So I can imagine why writers might not want to go through all that. Not everyone can have a platform to not only present their work, but to explain the unspoken neurologies or sexualities of their characters.
The best explanation of asexuality without using the word "asexual" appears in, of course, The Bone People. Keri Hulme writes this dialogue for her asexual protagonist, Kerewin:
I spent a considerable amount of time when I was, o, adolescent, wondering why I was different, whether there were other people like me. Why, when everyone else was fascinated by their developing nature, I couldn't give a damn. I've never been attracted to men. Or women. Or anything else. It's difficult to explain, and nobody has ever believed me when I have tried to explain, but while I have an apparently normal female body, I don't have any sexual urge or appetite. I think I am a neuter. (266)
The Bone People is a classic book, read by many people. I wonder what a sexual reader, unacquainted with asexuality, might assume about Kerewin. Of course, Kerewin lived in isolation in a remote area. It would be completely realistic for her to not have ever met anyone else like herself. While The Bone People was written in the 1980s, it's still realistic for an asexual person to have never met another ace, and to not know that there is a word describing their sexuality that is in use for other people. If writers want to be realistic, the unnamed asexual is much closer to the truth than the "out" asexual.
However, we're short on even unnamed asexuals like Kerewin. I think it's unlikely that a sexual author would write about asexuals. Most people haven't even knowingly met an asexual, so why would they write about one? But if "Shortland Street" can do it...why can't anyone else?