One problem with AI (vs e.g. Google search) is that there is no mechanism for attribution. So it is impossible for rights holders to understand whether their works are being monetised (unlike, say, Spotify).
Should NYT win, then either AI services will have to pay into a (very large) common pot for rights holders, which likely will make AI uneconomic (even if it does turn out to have some business benefit), or (paid) AI services will simply be banned.