As the sibling comment mentions, Stackoverflow would not know you have refused to save cookies on your previous visit, so it displays the banner again. That's precisely how it should be. If they want to know you without a cookie, they have to store your browser fingerprint, UA, IP,and more. I guess, that's not what you'd want.
If it has to be asked every time, then it could be easily classified as essential functionality and allowed. The rules are about sharing private / identifiable information, not about preventing client-side storage from working.
