I'm not sure why this alone is considered a separate issue from training the AI with books. Buying a copy of a copyrighted work doesn't inherently convey 'fair use rights' to the purchaser. If I buy a work, read it, sell it, and then publish a review or parody of it, I don't infringe copyright. Why does mere possession of an unauthorized copy create a separate triable matter before the court?
Keep in mind, you can legally engineer EULAs in such a way that merely purchasing the work surrenders all of your fair use rights. So this could wind up being effectively: "AI training is fair use for works purchased before June 24th, 2025, everything after is forbidden, here's your brand new moat OpenAI"
That has yet to be determined in a court of law. Just like: You can write a contract to kill but that won't make it legal.
The Supreme Court ruled that Fair use is an essential component that makes copyright law compatible with the First Amendment. I highly suspect that if if ever comes up in the SCOTUS they will rule that only signed contracts can override Fair Use. Meaning: Clickwrap agreements or broad contracts required by ebook publishers (e.g. when you use their apps) don't count.
Also, if you violate a contract by posting an excerpt of an ebook you purchased online would require the publisher to sue you in court (or at least force arbitration) over that contract violation. They could not use tools like the DMCA in such instance to enforce a takedown request.
There's no, "Hey! They're violating our contract, I swear!" takedown feature in contract law like there is with copyright law (the DMCA).