Ok. Then it's not about authors, but about copyright owners. Bit misleading to talk about authors, then.
FWIW it wouldn't work. The NYT and other newspapers have their whole archives to sell. A few months of a daily newspaper is more than even someone like Stephen Kind has published in his entire life. It's not even worth negotiating about such a tiny amount of writing. At best, you could do like with stock photography. They upload their texts to some website and accept whatever terms are offered. It might be a good business for some middle-men.
A prolific amateur might find it a welcome bit of extra cash. But the story doesn't stop there.
The extra costs must be passed on to the user. You transfer wealth from the public to a few large-scale owners, aka rich people. And since these AIs are text generators, you can expect that actual authors will bear the brunt of that.