It would increase privacy if we could protect with password the most important permanent assistant threads or folders.
The way it is now, all it take for someone else to read mine are opening a new browser window, search for anything at the address bar, and then going to assistant.
A user has a private conversation with an assistant, but doesn't want to lose the thread, as it may useful for him in the future. But also doesnt want other people with local access to his device to see the contents of the conversation. So he moves the thread to the password-protected folder.