If you read the complaint, it explains this pretty well. The use of copyrighted content by search engines is fundamentally different from the way LLMs use that same content. The former directs traffic (and therefore $$) to the publisher, the latter keeps the traffic for itself.

The legal misconception I want to flag in your logic is the notion that all uses of the Common Crawl are equally infringing/non-infringing. If you use the Common Crawl to create a list of how often every word in English appears on the internet, that’s unquestionably transformative use. But if you use it to host a mirror of the NYT website with free articles, that’s definitely infringement. The legality of scraping is one matter, and the legality of what you do with the scraped content is quite another.