First: There are mechanisms to opt out (robots.txt and meta noindex)
Second: There is some foreknowledge on the part of the web author. Even in the early days of the web — before you could’ve predicted the concept of search engines — in order to distribute anything you had to understand the basics of hypermedia, among which is the idea that anything can link to anything else and clients can be users or machines alike.
Third: Even though you are correct that search engines are tokenizing text and doing statistical analysis to recombine the tokens into novel forms in order to rank against queries, those novel forms are never presented to the user. Only direct quotes. So a user never gets a false reference to the supposed content of a page (unless the page itself lies to crawler requests).
Fourth: All of the technical points above are pretty much meaningless, because we are social creatures and our norms don't stem from a mechanical flow chart divorced from real-world context.
Creators are generally okay with their content being copied into search DBs, because they know it's going to lead to users finding the true author of those words, which will advance their creative pursuits either through collaboration or monetary support.
Creators are complaining about content being copied into LLMs, because their work will be presented out of context, often cited incorrectly, keep people away from the author of those words, and undermine the lifeblood of their creative pursuits -- be it attracting new collaborators or making sales.
Whether it technically counts as IP infringement or not under current law? Who really cares? Current IP law is a fucking scam, designed to bully creators out of their own creations and assign full control to holding companies who see culture as nothing more than a financial instrument to be optimized. We desperately need to change IP law anyway -- something that I think even many strident "AI" supporters agree with -- so using it as a justification for the ethics of LLMs reveals just how weak the group's position truly is.
LLM vendors see an opportunity for profit, if they can get away with it. They are offering consumers a utopian vision of infinite access to content while creating an IP chokepoint that they can enshittify once it blows past critical mass. It's the same tactics the social media companies used 15 years ago, and it weighs heavy on my heart that so many Lemmy users are falling for it once again while the lesson is still so fresh.