They aren't mutually exclusive.
Favicons aren't to give people a visual clue as to which site they are on, they are designed to be icons for your favorites list which is stupid: Other browsers put them in the tabs, or address bar, or even in the window-icon so you can find that web-application in your alt-tab list. Some web-application applications take advantage of this and animate the favicon so that people can know that a application desires attention. Others use the icon to indicate a logged-in or session state. This means that the favicon has become an additional graphic feedback mechanism.