If OpenAI owns a Copyright on the output of their LLMs, then I side with the NYT.
If the output is public domain–that is you or I could use it commercially without OpenAI’s permission–then I side with OpenAI.
Sort of like how a spell checker works. The dictionary is Copyrighted, the spell check software is Copyrighted, but using it on your document doesn’t grant the spell check vendor any Copyright over it.
I think this strikes a reasonable balance between creators’ IP rights, AI companies’ interest in expansion, and the public interest in having these tools at our disposal. So, in my scheme, either creators get a royalty, or the LLM company doesn’t get to Copyright the outputs. I could even see different AI companies going down different paths and offering different kinds of service based on that distinction.