Why do you think it would be illegal? You can state "permission is not granted to X" on anything you want, but that doesn't mean the law is on your side. Regular rules of copyright still apply.
P.S. Permission is not granted to downvote my comment!
Vitriol aside, you need to chill for a bit and touch grass.
"Training" doesn't really have a well-defined meaning, I could use your website to train something as simple as a histogram of word counts for an AI for example. Nothing about that constitutes copyright infringement under even the loosest definition of their legal concept.
Additionally weights from training and the AI's output are two completely different matters from a legal perspective as well.
I agree it is wrong and should be illegal. That being said, I do find the argument that's it's no different than a human learning from and occasionally reconstructing copyrighted things compelling.
Most normal humans do not spend their time profitably selling their "occasionally reconstructing copyrighted things" at a rate a millions of users per second, which is a pretty important difference in practice.
That said, the law is not made with super-humans being able to reproduce (slightly transformative) as good as all they read (all worlds' knowledge) in mind. A clarifying law should be created.
> Is it legal to transcribe a book from memory for money?
If it's an accurate transcription and you don't have permission, then it's not legal. It doesn't matter if it's for money or not (or if it's from memory or not).
> Does it matter how faithful your transcription is?
Yes, it matters. Copyright covers the specific expression of an idea, not the idea itself.
P.S. Permission is not granted to downvote my comment!