My personal prediction is that llm powered search will be as terrible as google search once people figure out how to game it. In a way probably worse because it will only give one answer instead of a list of answers that you can pick through.
For non current events I'll take a locally run LLM over privacyless google even if the results aren't quite as good. Google knows this and they are scared.
The only 'killer' use-case for LLMs is 'summarization'. That is it.