Why does Orianna need an autoatack damage booster?
Because Xypherous wanted to make a champion that didn't fall into the "shoot all abilities and then do nothing" pattern that he dislikes in a lot of combo mages. Given that he also wanted to make her a generally mid-range champion, giving her a reward for autoattacking was a very good way of giving her more to do in a fight.
Is there a reason she shouldn't have it? I never see Ori players bitching that they have to autoattack. They're certainly happy enough to autoattack people to death. Is there a real problem here?
Why does Shaco need an AP scaling trap, that is so strange it even has a build and playstyle dedicated to it?
Why shouldn't he have it? Allowing for different builds is a pretty damn good thing, and it fits his theme very well. Is there a reason you think he shouldn't have it?
Why does Cho need an autoatack trigger?
It gives him a consistent damage threat as a tank despite having skillshot based CC and damage, and it allows for him to be very mana-gated on his powerful skills while also maintaining a strong pushing pressure in lane. Tanks usually need some kind of consistent damage threat or very reliable CC in order to function. Cho's design explicitly lacks the latter, so he gets the former. As a side point, it also enables jungling. It doesn't have to be this way, but there's nothing wrong with his part of his design. It does the job fine. The only complaint I might levy at it is that it isn't set up well to be used by squishier Cho builds.
A better example of this problem would probably be Annie's E. There's a skill that really makes no sense.