We're already at the point where, for the vast majority of novelists (which is where I'm most knowledgeable), writing is not a primary source of income. With the exception of the very few bestsellers who are super-famous, most have other jobs or a spouse to provide income (and, in the US, health insurance). So most authors aren't doing it only for the money.
It's also hard to imagine a situation where authors are paid when AI ingests or remixes their work; this is already not the case. Legal cases have slapped down _piracy_, but it seems that _training_ is considered fair use, so long as the AI company buys at least one copy of the book.
There's no reason for the AI companies to bother paying anyone for their work.
But let's ignore all of that.
I write so I can tell the story. I write so other people can enjoy it -- so I can gross them out, or shock them with a clever plot twist they should've seen coming, or make them think about something differently, or let them have a moment of heartwarming joy, or just escape into a wild adventure of my own imagining. Otherwise, I'd just say "Odysseus had a long trip home" and be done.
If nobody reads my book unless it's been processed by an AI and mashed up with the writing of others... then nobody's actually reading _my_ book, and I see no purpose to throwing my work into the grinder.
Disclosure: I write novels, have one published, and plan to publish more, but I very much do not make a living off of them. Most of the (unlikely) futures in which I rely on writing income alone assume massive savings from my current tech job.