Animations were in vogue up until around half a decade ago and I'm glad they're dead. You still see them in older websites and in the efforts of amateurs who aren't making a point to stay on top of design trends, but menu slides and fades and so on instantly date an interface just like an "under construction" image or flaming skull gif.
Animations are difficult to reconcile with markup: ever played whack-a-mole with a menu that disappears as you try to move your mouse pointer over where you need to click? They are distracting and irritating for users, whose eyes are naturally drawn to motion and who have to wait for your animation to play out before they can get back to what they were doing -- fractions of seconds make a difference! And used carelessly they can easily render a website inaccessible for users with visual or motor impairments.
I agree on everything you said. Do you think there's a limit under which transitions are not disturbing? I think a good tradeoff would be under 200ms.
I think there could be. Where the threshold lies would be a great question for someone who actually studies and works with user experience, which I don't :)
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