I don't even think ownership rights are the principal component of this situation. It's true that in a different copyright regime, Anthropic could simply publish an archive of every book they scanned (and I think they likely would do that, if they could). But the primary reason these books get destroyed is that nobody cares about them. Old, rare books are a garbage disposal problem, not a cultural one. To me the most important thing to know about this story is that the AI companies are a tiny, tiny blip in the big picture of what happens to old physical books.

Everybody imagines libraries hoping against hope to get their hands on all these rare books so they can shelve them and preserve them for generations to come. But if you donate a box of old books to a public library, there's a good chance the clerical staff handling that donation is going to roll its eyes and cart the books out to a dumpster. Large public library systems have stopped taking book donations, for this reason. "Bring them to a thrift store" is what they'll tell you.