No one is pretending there are no "there are no negative consequences for the creator or the rights-holder". Of course there are. But this is a story of rights-holders, who've already outgrown their usefulness, wanting to tap themselves into money stream they are not entitled to.

ChatGPT isn't competing with NYT on a core competency. No one uses LLMs for original news reporting. They're obviously incapable of doing that, by virtue of not being there on the scene or able to independently research a topic, maintain relationships with sources, etc. What ChatGPT can do is quote/reproduce some parts of past articles, and reason from them. Or at least produce new text that's somewhat related to the old text.

The threat to NYT is this: ChatGPT is much better bullshitter than they are, so it reduces NYT to its core competency: providing original information. Which is all it should be doing in the first place. But instead, NYT wants to not only keep the bullshitting part of its revenue, but also take a cut or destroy the much greater and much more useful part of where this all feeds a general-purpose language model.