I agree that the Google business model doesn't fully accommodate conversational search UI, but LLMs can still play a valuable role in this area. In terms of a parallel, you can think of the "I'm Feeling Lucky Today" button as a way to bypass the standard search results and take a chance on a single, top result. Similarly, using LLMs in web search applications can provide a more conversational and personalized experience for users, offering a different way to interact with and find information on the web.

That being said, I don't think ChatGPT or any single LLM can replace mainstream Internet search use cases in the immediate future. They might enhance the search experience for users