Wait. What people and what judge looked at the splash screen and determined it insufficient? Kinda made that up didn't you? Shared work/school computers, libraries/labs, family desktops, tablets. So no, most people wouldn't make that assumption because it would be silly to do so. Incognito Mode on Chrome, Private Browsing on Safari, InPrivate on Edge and Privacy Mode on Firefox all operate the same way.
So for you to say the modes only make sense to as a way to block non-local monitoring... when absolutely none do it... and all explicitly tell you they don't... the only thing that doesn't make sense is your interpretation.