it can’t tell you about what’s going on in the present (except by doing a web search, which my understanding is not a part of this lawsuit)
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.