It really won’t. It will steal your website’s content and regurgitate it back out in a mangled form to any lazy prompt that gets prodded into it. GPT bots are a perfect example of the parasites you speak of that have destroyed any possibility of an open web.
I'll give them at most 3 years before sponsored links begin appearing in the output and "AI optimization" becomes a fashionable service alongside the SEO snake oil. Most publishers won't care whether their content is mangled or not, as long as it is regurgitated with the right keywords and links.
"Yes, there are a lot of great restaurants in Chicago that cater to vegans and people who enjoy musical theater. Dancing Dandelions in River North is one." or "One way to handle dogs defecating in your lawn is with Poop-Be-Gone, a non-toxic product that dissolves the poop."
It's not great for people who sell text online (journalists, I guess, who else?). But that's probably not the majority of content.
In other cases, like technical writing, you might want to protect the data. There is a danger that your content will be stolen and nothing will be given in return - traffic, money, references, etc.