IIUC that's not how this works, legally. The publishers have to prove damage; the defense isn't just automatically assumed to have injured the plaintiff. Even if IA has been proven to infringe, the judge can massively reduce awarded damages if they weren't actually hurt.
Furthermore, even if they didn't preregister, and they somehow cannot prove actual damages, it's still infringing conduct. They could, say, get a permanent injunction barring Internet Archive from operating their library program. This might actually be what they really want, moreso than money damages.
https://en.wikipedia.org/wiki/Capitol_Records,_Inc._v._Thoma...
Did they publish stats how often their most popular books were borrowed?
Don't libraries know the books they own? That seems unlikely, since they need to know that when they lend them out.
Just reaching out to all the libraries and getting them to submit the data would take a lot of time.
The problem is that they skipped that part and just assumed both that
1) libraries would transfer ownership to them. I could see them getting away with this. Inter-library lending is common.
2) the number of copies in partner libraries equalled the number of copies taken out. This is a massive assumption.
The problem is, did the books actually exist in the quantities being lent? IA has no proof that they do and had not transferred the rights for them even if they did.
Had they asked for libraries to upload their locked in inventory, sign away the rights to the inventoried books, and limited lending to that number, they could credibly call it controlled digital lending.
Instead they threw away the "controlled" aspect.