I'm curious what a use-case for this service would be. Why would I want to use some company's favicon for my own website?
A great example is 1Password, when you type in the url of an account, it fetches the favicon and displays it when listing your accounts, making is very easy to quickly scroll and recognize what you want.
It seems like something silly to depend on an external service for.
In addition to the other use cases already mentioned here, imagine an e-mail client such as GMail that - in lack of a photo of the sender - at least shows the sender’s company logo (which in many cases is the domain’s Favicon). In such scenarios Favicon Kit can serve as a fallback for services like Gravatar.
For me, I know having small icons helps me scroll through my bookmarks and identify resources I want to reference. Even if the shape of the icon is poor at a small resolution, I think my brain picks up on the color association. So just for the sake of finding things in my bookmarks, I can't imagine getting rid of favicons.
Having an icon for bookmarks and tabs is totally, 100% great - don't get me wrong. but they should be off by default.