I think I'd rather see cookie notices handled by a browser API with a common UI, where the default is always "No." Provide that common UI in a popover accessed in the address bar, or a side pane in the browser itself.
If a user logs in or does something requiring cookies that would otherwise prevent normal functionality, prompt them with a Permissions box if they haven't already accepted it in the usual (optional) UI.
There isn't any way EU didn't knew this was possible and is a better choice. There already was DNT header that they can regulate. It also knew the harm to ad industry.
Cookies for normal functionality don't require consent anyway.
But yes, I think just about everybody would like the UX you described. But the entities that track you don't want to make it that easy. You probably know of the do-not-track header too.