In the US, summary judgment is a procedure used in civil cases, typically one party seeking money from the other. Ineffective assistance of counsel is a criminal concept.
Not for civil cases. To win on summary judgment, there essentially has to be no genuine dispute of facts. So you often do not bother filing for summary judgment.
It's more appropriate when the dispute can be decided on purely legal grounds that don't need a juries input.
Ah, so basically the Internet Archive is asking the judge, "hypothetically, assuming we did everything they are accusing us of, we assert that the law would still be on our side, yeah?"
Whereas if the Internet Archive suspected what they were being accused of wasn't legal, summary judgement wouldn't be appropriate, and they might want to go to trial to try to prove their case that they aren't actually doing what they're being accused of?