In addition, the fair use test contains a pillar about the use not affecting the market for the copyright holder's works[1] which I think in google's case (and probably in the current openAI case too) seems obviously not to have worked out (ie google's use has demonstrably negatively affected the market for the original copyrighted work in cases such as news for example).
[1]: https://fairuse.stanford.edu/overview/fair-use/four-factors/
Most news sites wouldn't get any traffic without search engines and aggegrators. Which is why they are now whining about FB et al no longer sending them traffic.
And let's not forget that both traditional and online news is no stranger to republishing other people's content - one of the reasons fair use exists in the first place.
I have no love for big tech but let's not pretent that this is about anything other than news publishers wanting more gibs.
Google would argue (and they won in federal court versus the Author's Guild using this argument) that displaying snippets of publicly-crawlable websites constitutes "fair use." Profitability weighs against fair use but it doesn't discount it outright.
They would also probably cite robots.txt as an easy and widely-accepted "opt-out" method.
Overall, I'm not sure any court would rule against Google's use of snippets for search. And since Google's been around for over 20 years and they haven't lost a lawsuit over it, I don't think it's accurate to say "it's completely illegal if you think about it."
US copyright law is one of those things that might seem simple, but really isn't. Hence many of the copyright lawsuits clogging our judicial system.