I don't know why you do them. However I do them to fine tune my aim/cueball contact, and in the process check my alignment. If the aim looks wrong, or I seem misaligned, I get back up again.
I don't really "aim" as such when down over the ball, as much as I check that my cuestick is pointing in the direction of my aimpoint, which I picked out while standing upright. If my cuestick does not naturally "want" to point in the direction of my selected aimpoint, to me that suggests that my body is misaligned some way or other. If I just push the cue up to the ball and freeze it there, it will not show this misalignment as clearly as feathering will. We're not talking about major misalignments anyway, but a only a little bit. It is imperative then, not to force the issue, but instead get back up and start over. As you get better at the game, that should happen very rarely.
Anyhow the short feathers have many uses, and I don't see how one could prove that they have one use only. They obviously do what I stated above, but also loosen the arm/hand up. It's a good way to check if you are deathgripping the cue for instance (out of nervousness or other reasons), if you have problems with that. Very hard to do nice feathers with a death grip and too much arm tension, you'll feel it instantly. I'm sure many of you can think of other uses for them, but they work, that's the important thing.