Looks reasonable. So the issue here is that the icon= is a default value … the favicon isnt downloaded somewhere and then the path to the icon downloaded location isnt updated in the desktop file.
It’s an interesting thing to investigate. I suppose there could be many ways to slice this.
I would still dare to suggest that an extension for firefox would be the best way to address this in the interim. Such an extension would create a .desktop with the contents of the above and also download the favicon it’s available … both will need to be to a known location.
Bonus points would be for the extension to update plank if its running… or harder, add to the icon task list applet.