When an AI uses information from an article it's no difference from me doing it in a blog post. If I'm just summarizing or referencing it, that's fair use, since that's my 'take' on the content.
> having to pay for the trained model with them is not stupid?
Because you can charge for anything you want. I can also charge for my summaries of NYT articles.
A human makes their own choices about what to disseminate, whereas these are singular for-profit services that anybody can query. The prompt injection attacks that reveal the original text show that the originals are retrievable, so if OpenAI et al cannot exchaustively prove that it will _never_ output copyrighted text without citation, then it's game over.