anecdotal, but my wife wasn't interested in switching to claude from chatgpt. as far as she's concerned chatgpt knows her, and she's got her assistant perfectly tuned to her liking.
The only way OpenAI can survive is to replicate this model. But it probably doesn't have the traffic to pull it off unless it can differentiate itself from the already crowded competition.
But the thing is, the world already has an AI search engine. It's called Google, and it's already heavily integrated with Gemini. Why would people switch?
So I wouldn't worry about it.