Statues are 3-d and often life-like in their dimensions. Venerating something like that makes my teeth itch.
We can argue about style, but proper statuary is subject to the same rules as iconography and must convey the same theology. The Theotokos must point to her Son, for instance. It's just a different medium. Carved reliefs are not uncommon in Orthodoxy; why is the same graven image okay when they're it's halfway carved out of a surface, but anathema when it is freestanding?
A flat, painted Icon is clarly a likeness, not an attempt to recreate the physical presence full blown. So it is clear in a Icon that we are venerating a projection, an image of the that which is being venerated.
A statue is a projection in three dimensions rather than two.
A statue comes closer to the Pagan idea of the Statue being the thing itself due to it being made life-like.
Maybe in the ancient pagan mind with its superstitions, but I simply don't buy that idea in today's world.
Statues are old technology. How would you feel about venerating a Hologram that could move and react?
How would you feel about venerating a digital icon on a computer screen? Technology presents all kinds of problems when taken to their logical ends. I would not venerate a hologram, neither a flat icon nor a 3D manifestation, because they are not physical objects. Iconography does not exist merely to remind us of a person and focus our prayers; it is a physical touchpoint with the other world (if I am recalling my Florensky correctly).
As for moving and reacting, that is different, as it is an explicit attempt to simulate a living person. But if someone starts thinking a statue (or an icon for that matter) is alive and reacting to them, the problem is between their ears. As I said: on the whole, people are not likely to confuse a statue with a living being today as they were 1500 years ago, when people believed spirits literally lived inside statues.
I'm not saying we should replace icons with statues, or erect statues in addition to icons in our churches. I don't personally own any religious statues. I don't think statues have much of a place in the Eastern Church because it's not a part of our historical tradition. But is statuary somehow inherently anathema to the theology of the Incarnation that makes image-making necessary? No, I don't think so.