"If I'm a AI Bot operator/owner, I'm going to have my system scrape your entire website one time"
I can't work out if you're talking about the way that you imagine things work, or if you know how things work and are telling me this is how it's implemented at one particular "AI Bot operator".
Realtime search is an actual search of the internet, you can easily see this for yourself by asking ChatGPT what the weather will be over the next few hours. So I don't know what you mean by "My users are never going to trigger a real-time search of a website". Who are 'your users'?
I don't mean to be rude, but if you actually do know what you're talking about, I'm interested in what you have to say - can you cite some sources? Where did you learn about this caching mechanism you describe? Which chatbot vendors do this?
Anyway, it's irrelevant whether a search hits a cache or the internet, if a chatbot vendor decides that they want to pay 'per visit' then they can simply define a cache hit as a visit, there's no technical hurdle there. The real hurdle is the desire.
BTW you're incorrect that the 'future already exists'. You might be thinking of the present. The reason stage 3 is an issue for the future is described pretty well in that section, and I don't 'dismiss it' for any unreasonable reason.