I use the Gmail 'unread count' favicon labs option, which updates the favicon to reflect the unread message count in my inbox. It's an essential part of my browsing experience / daily workflow. The icon is correct when the tab is first loaded, but it never updates after that. Chrome and Firefox both implement this feature.
How have you used this in the past with Safari?
Since this is v1 of the feature (I know it's not all that advanced) I'm sure it uses simple caching rules to store the favicons. My guess is that eventually Safari will get the smarts to know when a favicon is marked as expired by the source site.
I've used this in the past in other browsers (Chrome / Firefox). A common use case is GitHub pull request status badges updating. I know this is v1 of this feature, I am just raising the issue so it can be fixed!
Just switched from Firefox to Safari and discovered with surprise that this feature is still not available!
While this is not publicly available feature for a reason, maybe there is an experimental toggle to enable it for specific urls?