A word salad of untrustworthy bullshit instead of the pages you were looking for is not going to upend search.
It's not a replacement for search in any way.
Now if the search engine could find pages which satisfy complex queries in natural language, referencing content and relationships among content, that could be something.
At best, you can have this: if it looks like the user is typing a question into the search box, an AI-generated side bar can complement the answers.
The web search side of it cannot go away, otherwise you just have a sophisticated Eliza.
If I'm going to see a factual answer, I want external references for those facts before I trust it. I'm likely not a subject matter expert, if I'm asking about something; I can't tell when the AI is bullshitting.
Now if the AI-powered search engine had an intelligent index of all the texts of all the crawled web pages such it could do some basic reasoning about it to serve up those pages based on sophisticated questions (and not simply serve up original prose based on those texts), that could be a game changer.