There are also some animations that that have utility beyond eye candy in communicating to the user what’s going on, which is particularly important for non-technical individuals.

For example the animation associated with minimizing windows in most desktop environments makes it crystal clear where your window went after you press the minimize button, even for novices. Removing that animation makes the interaction significantly more confusing.

Those animations are a no brainer because they both communicate something meaningful and don't get in your way. While the animation is happening you can keep working with whatever you were doing. I think a great UI can both be animated and allow you to work unhindered, if the designers put their mind to it.