Video calling may be a relatively new thing, but as Kottke points out, David Foster Wallace explored it in his epic novel Infinite Jest back in 1996. Here's why it failed in that book's world:
Good old traditional audio-only phone conversations allowed you to presume that the person on the other end was paying complete attention to you while also permitting you not to have to pay anything even close to complete attention to her. A traditional aural-only conversation [...] let you enter a kind of highway-hypnotic semi-attentive fugue: while conversing, you could look around the room, doodle, fine-groom, peel tiny bits of dead skin away from your cuticles, compose phone-pad haiku, stir things on the stove; you could even carry on a whole separate additional sign-language-and-exaggerated-facial-expression type of conversation with people right there in the room with you, all while seeming to be right there attending closely to the voice on the phone. And yet — and this was the retrospectively marvelous part — even as you were dividing your attention between the phone call and all sorts of other idle little fuguelike activities, you were somehow never haunted by the suspicion that the person on the other end's attention might be similarly divided.
[...] Video telephony rendered the fantasy insupportable. Callers now found they had to compose the same sort of earnest, slightly overintense listener's expression they had to compose for in-person exchanges. Those caller who out of unconscious habit succumbed to fuguelike doodling or pants-crease-adjustment now came off looking extra rude, absentminded, or childishly self-absorbed. Callers who even more unconsciously blemish-scanned or nostril explored looked up to find horrified expressions on the video-faces at the other end. All of which resulted in videophonic stress.
There's more at the following link (and even more in the book itself, natch): [Kottke]