There are some comments on the question which are quite telling - some people can get stressed or anxious when they have difficulty following the motion of an animation or sequence.
Yes, there is research to show that a faster animation is perceived as a faster application, but it is possible to animate too quickly, especially when the area involved is larger - filling a greater percentage of the view. This is especially important on smaller screens where the animation takes up a relatively larger proportion of the framed view.
The speed of an animation affects whether the viewer can identify a small part of the image transitioning, or the overall image appearing to flash or pulsate, with the detail being unidentifiable - a blur.
There are accessibility issues around making animations happen too fast, causing dizziness. Motion sensitivity and other vestibular disorders are often related to designs with parallax scrolling or badly timed animations, but when the user is focussed on small areas of pulsing animation, that can be problematic too.
For rotation where a dizziness or anxiety can ensue, that the rotational animation should either be avoided or counteracted with a balancing reverse direction motion to cancel out the directional effects.
So being 'smooth' and balanced is important so that the animation can be followed. This doesn't even require the whole thing to transition, but perhaps small elements moving within the whole can suggest a decent speed of progress without the whole image being distracting. I think this is why more 'interesting' animations are becoming more popular, where the loading image is made of individual animated components creating a balanced and harmonius movement within the context of the loader, rather than the whole loader shaking or rotating for example.
So in my opinion there is no right answer, since:
- I don't think directional spinners are a good answer in the first place.
- I don't think one given speed of rotation (or rather frequency) will be suitable for all, as different people have different perceptions and disorders.
- I don't think a 'whole image' transformation is the right effect.