Lack of a real delete option for Codex conversations is a privacy and user-control problem. Archive is not the same as delete. Users should have a clear way to permanently remove conversation history, especially when chats may contain sensitive code, project context, or personal information.
Have you tried asking Codex to help with this specific request? In practice, it is often capable of resolving issues like this on its own while we wait for the feature to be implemented.
Another option is to share your request to help the team prioritize new feature implementations: