I guess the main problem with the usual "they're a library" defense that IA usually gets to trot out is that their regular books usually are accessible under a lending system - that's to say, they manually digitize the books and don't let people read more copies than they have on file[0].

This system as I understand it doesn't apply to any of their non-book collections (not to mention it only applies to files that IA has uploaded themselves, the archive also accepts user submissions).

Fair Use is very unlikely to apply here I think. The fair use test looks in part at the question of how much of the copyrighted work is distributed (ie. A radio program promoting a song with a short jingle has a much more solid defense than others.) and "all of it" isn't a good defense. They could've put these recordings under their usual lending system, but they didn't and that probably makes them liable.[1]

For reference, I am not a lawyer, so if you think this is legal advice, go talk to an actual lawyer.

[0]: The ebook lawsuit they recently lost was because they disabled all lending restrictions for the pandemic, triggering the lawsuit. The lawsuit itself is ballooned with other crap because the usual nonsense from publishers is a thing, but the grounds for the lawsuit were unfortunately very solid.

[1]: That said, this lawsuit was probably triggered because the judge in the ebook case partially stripped IA of its library protections. The record companies probably are trying to arrange a similar removal of protections from IA, hence why this specific collection was targeted.