There is already a business model for compensating authors: it is called buying the book. If the AI trainers are pirating books, then yeah - sue them.
There are plagiarism and copyright laws to protect the output of these tools: if the output is infringing, then sue them. However, if the output of an AI would not be considered infringing for a human, then it isn’t infringement.
When you sell a book, you don’t get to control how that book is used. You can’t tell me that I can’t quote your book (within fair use restrictions). You can’t tell me that I can’t refer to your book in a blog post. You can’t dictate who may and may not read a book. You can’t tell me that I can’t give a book to a friend. Or an enemy. Or an anarchist.
Folks, this isn’t a new problem, and it doesn’t need new laws.