Another thing about the Sky Forme restrictions: a lot of them basically caused some of the sprites to be changed/made worse just to make them appear to be flying. Just look at Xatu – its design is clearly based on a totem pole (among other things, of course), and all the past-gen sprites and Sugimori art depict it in its totem-pole pose. But to make it eligible for Sky Battles, they had to change its pose to be flying, which makes it lose a lot of its 'mystical' effect. It was designed to be viewed body-on, not beak-on.Basically the Flying-type and Levitating Pokemon they don't allow have their animation standing on the ground and not actively flying/levitating. This basically restricts the first stage evolutions of Flying-types (and Doduo & Dodrio, but that makes sense. Also Hawlucha) which I guess isn't that big of a deal, but there are still a few odd restrictions: Farfetch'd, Gengar (even though Gastly and Haunter are allowed...), Delibird, Chatot, and Shaymin Sky Forme. Also, though they restrict some first stages, the allow others like Zubat, Ledyba, Hoppip, Wingull, and Swablu.
To tell the truth, I'm not entirely sure why Sky Battles were added – they're used only by a specific kind of trainer, and after you beat all of them, you can never have another Sky Battle. Ever. Even though Inverse Battles are only performed by one person, you can at least do them as much as you want.