I wasn't aware Firefox did this. I was using Opera until a few days ago so this information is news to me. I know Opera stores icons on the hard drive. I had to free up some disk space on an old computer I was using a couple years ago when I discovered that the Opera icons folder stored thousands of icons taking up a large amount of space. I had to find the folder where they were contained and delete them manually. I'm not certain about Firefox, but from the links below it appears the icons may be stored as binary data in an sqlite database in the profile folder for Firefox. A post on the Mozilla support board seems to confirm this is where icons are stored. The first link provides info about how to delete them with instructions how to first backup your bookmarks and re-import them as HTML without the icons. You could also wait and see if the add-on author updates so it works with Firefox 22.
The Firefox sqlite file is already over 10 MB on my computer that I have been using for 3 days. I can't imagine how big it will be in a year.
Maybe these instructions will work for disabling favicon storage. I will try it later.