They’ll certainly try, though it’ll be quite a bit trickier due to LLMs providing direct answers, not just a list of sites. You can’t really sneak a product in there when it doesn’t actually fit the question. I think the bigger problem is just the lack of good information out there. Finding trustworthy reviews these days is getting really hard, most of the time all you have is the product description and some Amazon reviews, which even when done well, fail at providing how product X compares to product Y. No matter how smart the AI will be, that always leaves a ton of room for error and misinformation.
Hard to tell how things will end up. For the time being, LLMs are pretty much completely useless for product search, ChatGPT just doesn’t know enough and BingChat will just summarize the first three SEO-filled Bing search results. The deep knowledge LLMs have on Wikipedia-like topics is missing when it comes to products and services, and they can’t really do calculations either, so price information is almost always wrong. This will need some specific optimization.