I'm not sure I'd appreciate this feature. When I used LLMs I found conversations got more difficult the longer they went on - I'd ask one question, then another, and it'd try its best to answer the latter in the context of the former in a way I didn't intend. I used new chats as an explicit way to escape this. I also created new chats when I felt the LLM was going down the "wrong path" or generally interpreting things obtusely.