I am really enjoying this thread!! I thought I would chime in with my VERY limited experience and observations with what I like to call my "Lord of the Flies" flock (they're all the same age (9 months old) and have grown up their whole lives without older hens/roosters. They have been free ranging since they were 3 months old).
I have two roosters in my flock of 19, one is the dominant flock master, the other is very submissive but has made a few surprising and bizarre attempts to overthrow the alpha with very little success. Most of the time sub just runs away from alpha.
@Perris I do believe I have observed the similar kinds of wing dancing to what you're describing with Hensol and Killay. Particularly, I have seen specific cases where a hen will call out for a rooster to come and fetch her either after she's laid an egg or gotten lost from the flock somehow. Both roosters will take off running toward her, but alpha will actually stop and wing dance around submissive roo. Submissive will dodge him just like a hen would when wing danced at and will stop running toward the hen in need. The alpha will then go and collect the hen (funny enough he wing dances at her as well to herd her back) while submissive boy goes back to the flock. There's never a fight (at least that i've witnessed). I always read those interactions as alpha telling submissive that he's the boss around here and submissive mostly obliges without a fight.
So as far as I've observed, I think you may be onto something where the wing dance is actually to "encourage submission without a fight". That's mostly how I've observed my alpha using it with the submissive cock and with the hens.