they DO have this feature: a way to open a window that leaves no history

"You've gone incognito. Pages you view in this window won't appear in your browser history or search history, and they won't leave other traces, like cookies, on your computer after you close the incognito window. Any files you download or bookmarks you create will be preserved, however.

Going incognito doesn't affect the behavior of other people, servers, or software. Be wary of:
Websites that collect or share information about you
Internet service providers or employers that track the pages you visit
Malicious software that tracks your keystrokes in exchange for free smileys
Surveillance by secret agents
People standing behind you
Learn more about incognito browsing.