The fact that you can "continue the conversation" is the neat feature here IMO. Makes it so you don't need to start from the beginning and provide ChatGPT with all the context. Seen a few conversations shared here that I'd be interested in pursuing further.

It also means our conversation is recorded by openai, doesn’t it?

Chat history can be disabled in the settings menu, temporarily or permanently at least for Plus users, not sure about free users…

You have two options in the settings menu:

1. Share all your chat data with OpenAI

2. Disable saved chats entirely.

You want to have saved chats but don't agree with OpenAI also having access to them? Not possible.

I use ChatBot-UI to achieve something like 1 and 2 together. It runs locally and uses the OpenAI API to provide a ChatGPT-like experience, but the chat history is saved locally in the browser. It also has a useful prompt management sidebar.

Of course, OpenAI saves the data regardless, but they say they don't use API requests for training data and they claim it's deleted after 30 days.

https://github.com/mckaywrigley/chatbot-ui

https://openai.com/policies/api-data-usage-policies