so, that being said, with regards to your main points:
your note on depth perception is right on the money, I think. it seems reasonable to claim that, in lieu of being able to accurately make a quantitative estimate, the player must fill in the gaps somewhere else. it would seem that this could either come from history (either map knowledge, which I think is significant--think golf courses, right? or a more local sort of history like you point out: just the previous shot) or perhaps some kind of live prediction.
the thing is, the bullets (or the gun, depending on how you see it) have a fixed velocity, and as my partner Elliot pointed out several times, that gives them an inherent 'working range'. the gun we shipped with has a sweet spot, a range (I dunno, something like 4-12 meters) where curves are relatively easy to control and the margin of error is (or so we hope) reasonable. outside of these ranges it begins to get difficult, more like a 3 pointer in basketball, and you have to compensate in other ways. so the golf club analogy kind of holds, in that there's a spot you want to hit which provides its own margin of error (the size of the enemy), and a 'club' that has a sort of working range and height (the gun).
the real question I think you're getting at is whether it's reasonable to expect that, as a player, investing your time in practicing this weird thing has any promise of making you any better at it. you're alluding to the potential existence of a sort of physical barrier--either in humans or in the game's presentation--that means your experience will just eternally be suboptimal and therefore unfun. and how can you know for sure, given that a hundred guinea pigs haven't come before you and proven that it can be done? if I were you, I'd be suspicious.
I'm not sure that I have a direct answer. but I do agree, and you are making a good point, that we pile on a lot at once. stick peeking and particularly stick dodging I believe feels rewarding once you get into it--and motivates the controller as an input method--but for new players, becomes just one more thing to manage while dealing with the already very hard shooting scheme. designing play environments (as you say) around some of these more basic concepts seems like a valuable direction.
thank you again!