It's actually quite a difficult problem for the browsers themselves and they have all the information that's available. There have been a lot of issues with showing the new URL while the old page is still in the browser, for instance.
Having special cases for every exception doesn't scale. What about Outlook Web Access using Microsoft accounts or domain accounts? Are you going to build an add on for every webmail installation?
That's the point of having an addon API instead of fixed behavior, to implement logic around such complications.