Let's say I host these, offer some indexing on it, and rewrite articles. Something like, summarise all articles on US-UK relationships over past 5 years. I charge money for it, and all I pay NYT is a monthly subscription fee. To keep things simple, let's say I never regurgitate chunks of verbatim NYT articles, maybe quite short snippets.
Is that fair use? IANAL, but doesn't sound like it. Typically I can't take a personal "tier" of a product and charge 3rd parties for derivatives of it. Say like VS Code.
A sibling comment mentions search engines. I think there's a big difference. A search engine doesn't replace the source, not at all. Rather it points me at it, and offers me the opportunity to pay for the article. Whereas either this or an LLM uses NYT content as an alternative to actually paying for an NYT subscription.
But then what do I know...