I think we need a lot of clarity here. I think it's perfectly sensible to look at gigantic corpuses of high quality literature as being something society would want to be fair use for training an LLM to better understand and produce more correct writing... but the actual information contained in NYT articles should probably be controlled primarily by NYT. If the value a business delivers (in this case the information of the articles) can be freely poached without limitation by competitors then that business can't afford to actually invest in delivering a quality product.
As a counter argument it might be reasonable to instead say that the NYT delivers "current information" so perhaps it'd be fair to train your model on articles so long as they aren't too recent... but I think a lot of the information that the NYT now relies on for actual traffic is their non-temporal stuff - including things like life advice and recipes.
The case for copyright is exactly the opposite: the form of content (the precise way the NYT writers presented it) is protected. The ideas therein, the actual news story, is very much not protected at all. You can freely and legally read an NYT article hot off the press and go on air on Fox News and recount it, as long as you're not copying their exact words. Even if the news turns out to be entirely fake and invented by the NYT to catch you leaking their stuff, you still have every right to present the information therein.
This isn't even "fair use". The ideas in a work are simply not protected by copyright, only the form is.
As a counter argument it might be reasonable to instead say that the NYT delivers "current information" so perhaps it'd be fair to train your model on articles so long as they aren't too recent... but I think a lot of the information that the NYT now relies on for actual traffic is their non-temporal stuff - including things like life advice and recipes.