This is an interesting thread
the confusion is understandable. The lack of three dimensional statuary has nothing to do with residual iconoclasm although I guess I could see why the idea came about. After all, we kiss icons with abandon, I have never seen statuary or pictures kissed in a Western church.
Icons are not decorations either, although they can be decorative. Think of it like the Rosary cord, it is functional and the believer will actually kiss the crucifix before and after using it but some people will merely display them. Same with an icon, same with a Bible.
The fact is that the theory around which icons are used and produced is a bit complex, I am not capable of addressing this issue appropriately, so I would suggest further reading.
The ancient Greeks had certainly mastered the production of the idealized, yet realistic human form in three-dimensional statues. The Byzantine Greeks continued to produce these for public display all through their history, there was no cultural aversion to them. If statuary was useful, the Fathers of the church would have wanted them in the temple, but statuary cannot be used in Byzantine temples liturgically, let me try to explain.
As I said icons are not mere decoration, they have a dynamic component to them. They are written, not painted, according to some strictly defined rules. The iconographer is supposed to fast before starting an icon and pray continually during the building process.
The icons are like windows, a way of seeing what you know to be actually there anyway in another dimension. Icons are written in such a way that they give the impression that the subject is aware of the observer, so there is actually a two-way traffic there. Most subjects are portrayed frontally, not in profile so it is a lot like one person standing before another, and the exclamations of prayer can be like talking between people. Christ Himself is often portrayed with one eye looking directly at the observer and one eye looking beyond, as the One who sees right into you and all your sins yet also looks beyond all that, the effect can be stunning.
Christ Himself, in the flesh is an icon. He is The window for all to see God.
Two dimensional imagery is more useful than three dimensional imagery for this iconic depiction, especially since realism is not the first priority. Not all items depicted in an icon are in proportion, there is a tendency to depict things as greater or lesser in size to reflect their importance, it might not be immediately obvious but that will likely have a subliminal effect in telling the icon’s story, and icons are full of information.
Ordinary saints (bishops, priests and others) when in the presence of the Supreme Holiness are always depicted with their hands covered. It shows they are not worthy enough to presume to touch God.
The gold background is a way to depict eternity, or beyond time and space. Why is this important? Because the liturgy itself is the intersection between our world (in time and space) and the eternal realm, it happens right there, as in a cosmic zone, one is neither here nor there and we are joined by Our Lord, the saints and angels and all worshipping believers of all time, past and future! The icon is not a representation of these subjects, but a window into eternity where we see them for ourselves.
The liturgy is another important subject that should be considered along with iconography. It is a multi-sensory event. One is immersed in sights, sounds, smells, taste, touch and raw emotion. The intellectual component is supplied by the prayers and supplications which reflect what we believe and have always believed, long term worshippers internalize these ideas through repetition,
Lex Orandi - Lex Credendi. The liturgy is like the worship described in the Revelations of John, if you come to observe (you are most welcome to), keep that in mind.