I'm gonna just say the more I use ChatGPT, the more I don't want it integrated with search.
I want search to be a different tool. I want to switch to search so search does it's thing well. It finds real content and helps me evaluate what ChatGPT is saying. They compliment each other really well, but they feel like fundamentally different interaction modalities.
To the extent chat is integrated with search, I don't want to know that it's there. Like good CGI, it should just enhance the existing experience, not insert itself into the conversation.