This is a negotiation tactic by the NYT to drive up the licensing price. Period.
The Napster/Music Industry analogy has no resemblance to this situation.
The only meaningful question that might be answered as a result of this is, what permission and access rights do crawlers have to content that is publicly and legally available.
NYT is paywalled - you have to agree to a license to access it, there are exclusions in that agreement that I don't understand but I think may be important in this discussion!
There appears to be an open question about if the LLM can freely ingest copyrighted material and output it verbatim without violating copyright. That seems like an obvious "no" to me, unless we decide that LLM has special treatment.