Was an article added to the list during a refresh? Did the correct item actually go away after deleting it? It's easy to miss updates without animations. Even if you don't miss the update an animation will provide an additional confirmation that the correct thing happened.
On touch devices there's also the fact that animations mimic input gestures. Imagine swipe-to-delete without the item actually moving, that would be super awkward to use...
Of course, like anything, it is possible to mis-/overuse.
I suppose you could just about make a case that when you have a modal element like a form to edit an item, if it takes up most or all of a small screen then having an animation to expand it makes a visual difference between "you're now on a new page" and "this form has popped up, but when you close it you'll be back on the page you were before - it hasn't gone away".
Otherwise mundane app will look much more sophisticated. It can also make the experience more fun, which makes it easier to addict the user. Just think why slot machines are so colorful and flashy. Would they have same appeal if they would look and behave like a parking meter?
I would not mind animations if:
- they would not slow me down - I'm faster than them and I have to wait. It would be interesting if animations would be faster or disabled when user interacts faster than some threshold.
- they would be interruptible
- they would not cause performance degradation
- they would not add more bugs. As with most asynchronous actions they are not properly tested when things happen simultaneously or are interrupted.
Though it may be interesting just to let users choose whether they want to see animations in general. That'd solve a lot of problems here, and additionally give you some metrics in regards to how many people like the things.
That would be the ideal solution. Make a setting in browsers and devices where users could turn off all animations. Designers could test their UIs with the setting on and off. Everyone would be happy.
Except when there is - for example, first-user introduction/onboarding segue's, which guide the users attention around the app by highlights/flows, perhaps overlaid in a fashion that makes it clear that the overlay itself is impermanent (by fading it) .. but only if its got a real purpose, as you state.
I appreciate this degree of assistance in learning a new app personally, especially on mobile.
Animating the UI is what we want the user to do anyway - and many users are very animated about how they use their apps (i.e. selfie culture), so using animation to train the user to use the app properly, such that the user animates back, seems obvious.