alt Hacker NewsAnimations are highly effective tools for conveying state information.
Consider a toolbar with a mix of enabled and disabled buttons. Hover effects (which I would consider animations) convey that something is clickable, and on-click effects confirm an action. These effects convey meaningful information to both beginner users and power users of any software, and are in no way inconvenient to either group.
I generally agree animations tend to get in the way when you want to get shit done, but the idea that animations are only applicable as artistic effects rings untrue to me.
Hover effects are a terrible way of indicating if something is clickable, because you have to mouse over them instead of just looking at them. This problem was already solved a long time ago by rendering inactive elements in gray. I'm not sure which GUI did this first, but the Apple Lisa (1983, first mass-market personal computer with a GUI) definitely did it.