Favicon or Web site icon

When dragging shortcuts to the desktop we always get the Dragon Icon for all sites.
It would be nice to have the websites favicon as the saved icon like IE and Firefox does.
As it is now we have to read the description under the icon to know where it came from.
With the favicon for example Googles icon would be a G. And Microsoft’s icon would be the four colored squares.
Then we could tell at a glance what site the shortcut belongs to.