A lot of search results quality is based on perception and trust. For example, bing ran multiple studies where its results were as good as Google in blind tests. Still, instinctively, people flock to Google.
Point is that if people suddenly trust chatgpt based on marketing or some pointed queries, they would simply go there and not pick a case by case where chatgpt does better than Google or not.
Also, I think you are being a bit harsh. If u are trying to prove chatgpt wrong, sure you can, like in the case of goat eggs example. But, the use cases where you search and land up on a random website, chatgpt takes the cake for me. I don't need to go to a random website, bypass their random ads and then try to read the information. chatgpt right now does all of that for me.
Me thinks, whether chatgpt succeeds or not, it will make a big dent in the way we get information in the next year. And things are already moving in that direction!