Why do I get the feeling millions of people are going to start losing their jobs over this in the next few years?
Because that's what's going to happen.
I don't think they'll be directly replaced with AI though. Instead the company they work for will go bankrupt because they can't compete with competitors who figure out how to improve productivity using AI.
It's absolutely part of the lawsuit. NYT just isn't emphasising it because they know OpenAI is perfectly within their rights to do web searches and bringing it up would weaken NYT's case.
ChatGPT with web search is really good at telling you what's on right now. It won't summarise NYT articles, because NYT has blocked it with robots.txt, but it will summarise other news organisations that cover the same facts.
The fundamental issue is news and facts are not protected by copyright... and organisations like the NYT take advantage of that all the time by immediately plagiarising and re-writing/publishing stories broken by thousands of other news organisations. This really is the pot calling the kettle black.
When NYT loses this case, and I think they probably will, there's a good chance OpenAI will stop checking robots.txt files.