Will they though? Last I heard OpenAI isn't profitable, and I don't know if it's safe to assume they every will be.
People keep saying that LLMs are an existential threat to search, but I'm not so sure. I did a quick search (didn't verify in any way if this is a feasible number) to find that Google on average makes about 30 cents in revenue per query. They make a good profit on that because processing the query costs them almost nothing.
But if processing a query takes multiple seconds on a high-end GPU, is that still a profitable model? How can they increase revenue per query? A subscription model can do that, but I'd argue that a paywalled service immediately means they're not a threat to traditional ad-supported search engines.