Seems like an open question as to whether that violates any laws.

Another way to look at it is that if you publish a service on the web, you have limited rights to restrict what people do with it.

Isn't that the logic Google search relies on in the first place? I didn't give permission for Google to crawl and index and deep link to my site (let alone summarize and train LLMs on it). They just did it anyway, because it's on a public website.

Google's stance is "I can copy you and you can't stop me" as well as "You can't copy me, I'll sue you"