Search engines are just cheaper to run. I don't know that there's a good, long term model for a free LLM-based search replacement because of how much higher the operating costs are, ad supported or not.
It could also become a differentiator allowing multiple suppliers. On one hand, you have people doing search for quality results. Other search engines include the AI results. The user could choose between them on a job by job basis or the search provider might, like !G in DDG, allow 3rd-party AI search as an option.
The bigger problem I have is with scale for the dollar. Search companies with their own indexes already mostly failed. There’s a few using Bing. It’s down to just three or four with their own index. Massive consolidation of power. If GPU’s and AI search cost massively more, wouldn’t that problem further increase?
To be clear, I'm not arguing for everything should be part of a pretrained LLM, but the experience of knowledge searching that ChatGPT and Perplexity provide are pretty superior to Google today (when they work).