This isn't theoretical, AI companies have finished lawsuits about this and this was the ruling.
A person can digitize their own books without destroying the original. So can Anthropic. They are choosing to destroy the books for easier scanning and trying to palm off the blame for it.
I'm old enough to have been around when DCMA legislation was under discussion. Many people were dead-set against it and raised concerns over matters exactly like this. In Rainbows End (2006), Vernor Vinge wrote about a similar scenario where a robot went through the university library shredding books, and scanned the shredded pieces to recombined them into a digital archive.
Anthropic may be doing shady things and may have even done this on their own recognizance, we just don't know. As it stand, this is 100% a consequence of US copyright law, much of which was written by large corporations to protect their own assets.
You’re missing the point. It doesn’t require that they destroy the book, but it precludes them from giving it away. It’s their property, so they can choose to store it, but that has real, ongoing cost and may eventually leave unusable books anyway due to fire, pests, water damage, etc. if they’re not maintained properly.