But then the AI is the writer and you're just an editor or curator. So perhaps don't call yourself a writer if the AI produced a significant amount of the content. Same goes for Stable Diffusion/Midjourney prompters who shouldn't really call themselves artists. (Things would of course change if they do significant postprocessing of the output, though I'd still think this is much easier than coming up with something novel on the spot.)

Of course, it's not my place to say who should or shouldn't call themselves a writer, but I'll simply personally respect someone more if their stories aren't ghostwritten by the AI.