I was always curious why is it called Incognito or Private mode? Temporary or Guest session would make more sense: "You've entered a Temporary session. Your browsing history and cookies will not be saved."
Guest sessions already exist in the profile menu and is a separate feature. Guest doesn't save history/cookies/etc locally but also doesn't use your existing history, extensions, bookmarks, settings, etc. It's intended more for an actual guest user to sign into temporarily.