I'm not sure the analogy really fits. As I see it, hypothetical farmers aren't an elite class that gets rich from copying and transforming the communications and creative output of billions(?) of unknowing people.
When LLMs reproduce someone else's work, it is theft and appropriation, and our tech culture is rationalizing it out of hatred of the laptop class -- the kulaks, in my analogy. These traditional media do have their faults, and it's fine to point those out. But reporting is work, consisting of more than just "copying and transforming", and stealing it is wrong. "[F]orcing" it into the public domain is no more a "best outcome" than forcing the farms to collectivize.
I'm going to go out on a limb and say that solution wouldn't be acceptable to the NYT, which is why I think they're trying for a land grab. They're trying to extend copyright beyond what was intended.