You are assuming LLMs will replace search engines. Why is this the case?
To me it seems like there has to be so much optimization for this to happen that, it is not likely. LLM answers are slow and unreliable. Even using something like perplexity doesn’t give much value over using a regular search engine in my experience
LLMs will not fully replace search engines, but Google and Bing are evolving to be LLM first, anyhow. So "what is a search engine" today is not what it was yesterday. Let's call the time before LLMs, traditional search. LLM first products bundle some aspect of traditional search. And traditional search is adding LLM answers.
Traditional search will still be highly useful for transactional, product, realtime, and action oriented queries. Also for discovering educational/entertainment content that is valued in of itself and cannot be reformulated by LLM.
To me it seems like there has to be so much optimization for this to happen that, it is not likely. LLM answers are slow and unreliable. Even using something like perplexity doesn’t give much value over using a regular search engine in my experience