This is the Geocities of vector art. I don't see this as a good thing, I see this as a poor compensation for bad interface design. If your icon needs animation for it to make sense to your visitor you're doing it wrong.
That seems like a generalization. Surely there are instances where animation is appropriate for an interface. What's so wrong with another tool to achieve that goal with the added benefit of being entirely scaleable?
Animation is suitable in an interface, an icon does not constitute an interface. An icon on a button animating on rollover is just distracting. Now, perhaps if something had to go on in the background it would be relevant (indicating that the work is still in progress) but that's a very edge case.
Drag and drop. When I drag an icon to a location and I miss, I think it's better to see the item animate back to it's original location rather than just disappear and "pop" back.
Having it animate back is just better communication for that particular interface.
You can see this on Google Chromes new tab "Most Visited" page, drag an item and let it go on nothing, it will animate back to its position.
Then there's sorting, it's much better (to me) when the interface animates to show you what the effect of moving one item to a new location will have on the rest of the items in that list, you can see this effect on sites like Trello when you drag around cards, etc.
I'm sure there are more examples of good uses of animation in interfaces.
Why not? Say someone is designing a weather app where they want to show active snowfall - an animated vector icon showing falling snow communicates that perfectly.
