Much debate has been had about how existing copyright law applies to AI models. But once you get past that and start asking about how copyright should apply to AI models (as the copyright office is here) the answer in my mind becomes clear. Copyright, as defined in the U.S. Constitution, exists "to promote the Progress of Science and useful Arts"[1]. I can think of no better modern example of "the Progress of Science…
Your point 1 is what concerns me. AI models seem too much like the printing presses of old. They are available mainly to corporations and authors need to be protected from them. Otherwise there will be no incentive for anyone to publish anything novel as they know the corporation will slurp it up and make it "better" with their better model.