I'm enthusiastic about animation support. It's mind-boggling that we are still using an image format from 80s with crappy compression and limitation to 256 colors.
The only thing I can think of off the top of my head where it's preferable is if you needed to do a video with an alpha channel. But this is more codec related than a problem with the concept itself.
Animated images have several advantages:
-Almost all places that support images support also animated image
-Can be downloaded and reposted (as opposed to canvas)
-No worry about audio, there is no audio
-Seamless looping
-Auto play everywhere
-Variable frame rate
These features could be achieved in a video format, but how would you convince websites that support images to support video with these characteristics?
For example, I would never let people upload autoplaying, looping videos as their avatars or as part of their comment unless I could be 100% sure that there will be no audio. I would have to inspect the video for audio and I would need different handling for images and videos.
Have you seen how people use gif animations?