That does not prove that Ameratasu appears instantly at its target. Your suggesting that it's some kind of S/T dojutsu formed from the eyes onto its target. I have never seen this stated in the manga. And based on the fact that Nagato said the air pressure changed when he thought Itachi was about to use it I would think its merely a high speed attack. Your also assuming that Sasuke can use Susanoo on his Hawk. This also has not been shown in the manga. I would also consider this very unlikely as a chakra mass like Susanoo has weight. And given that Susanoo is not known to be able to move very fast I highly doubt that a Hawk can carry Susanoo or at the very least be able to fly with something that big on its back. As to the arrow arguement the sand ball is not stationary in the air so it is unlikely that it can hit when Gaara has 360 degrees of movement.I had to respond to this considering this post has a lot of flaws in it. For one amaterasu instantly appears wherever the user looks regardless the distance.
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Amaterasu doesn't travel.
Secondly the arrows are made of chakra so it makes no difference where they're traveling whether it's the ground or in the air. I don't know what kind of logic that is.
Thirdly where is it ever stated susanoo can only be used on the ground? Madara has had no problem forming and using it in mid air. It's pure chakra meaning Sasuke should have no problem being able to use it on his hawk.
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And lastly not many shinobi have fought against an Uchiha with the MS. Sasuke has that and tsukuyomi comes along with it. Yes it may not be as potent as Itachi's, but it does still paralyze anyone it hits as it did with Bee before the hachibi woke him up from it. I was only saying that not all shinobi can fight looking at someones feet as Guy can, so it's not logical to bring that into a debate when discussing an uchiha vs whoever.
As to genjutsu if he had the chance to beat Gaara, Mei, A, and Onoki with it then why didn't he use it? He was fighting with all of them and was looking them in the eyes.