> In fact I can't think of a single good design reason to ever animate an icon

I can think of a few cases where animated icons make sense.

1. Control feedback. If your icon deforms slightly under your mouse when you click, it provides extra feedback indicating that your action was registered.

2. Notifications. As you, yourself said, motion catches attention. So animated icons would serve well for any kind of event notification. New message or event, action completion etc.

3. Progress indication. An icon for something that takes a long time, like a file download, could be animated to indicate that the process is still ongoing.

I am sure there are other examples.