Motion is extremely effective at drawing the eye's attention, and so should never be used unless that's the goal.
In fact I can't think of a single good design reason to ever animate an icon except for loading/progress icons, which already are ubiquitous and generally don't need any dedicated animation tools since they're so simple and reusable.
You don't ever want normal interface/page icons to be animated constantly, because it's always distracting and never good.
What about intermittently, like hover states? Still no, because a hover state exists to give confirmation that you've mousedowned on a clickable area -- so the hover needs to be an area-wide confirmation (like changing the button color). Animating an icon instead is too confusing, and animating it on top of a color change is too redundant and noisy.
So I just don't see any use case at all.
(Extra note #1: motion itself can be helpful in UX -- e.g. an icon expanding in size to a card, a card sliding off, etc. -- but none of that involves animated icons.)
(Extra note #2: except for gaming interfaces which are all about sensory excess -- shadows! sounds! animated icons! pop-out effects! -- but those tend to be based on other technology workflows anyways.)