Earlier quoted context omitted.
Greasemonkey extension with some script like https://gist.github.com/robbyrussell/46193 (I didn't test it but it should work)
Ah, a script/plugin as a workaround? Maybe, but do the sites with animates favicons deserve so much attention? Do you know any useful web site with animated favicon?
Lichess, and some messengers like telegram and whatsapp web clients.