Aside from aesthetics, the primary purpose of live rock is to provide nitrification and denitrification, particularly denitrification. On the reef the two occur more or less simultaneously. Where ever nitrite is created, there's denitrification bacteria nearby that quickly consume the nitrate.
In a substrate-less tank, most of this occurs on a thin veneer of rock. There's little denitrification deeper in the rock because the nitrite is consumed before it can penetrate the rock, so we don't need as much rock as has been preached even in a substrate-less reef tank.
In a tank with substrate, the rock is even less useful. Most denitrifacation occurs in the sand (and even gravel). The reason most denitrification occurs in the sand is that diffusion is greater in sand (not so much because of the greater surface area, although the two are related). That is, the nitrite can reach more bacteria in sand than in rock. Since the bacteria gets first dibs on the nitrite by virtue of water motion, there's little left that is broken down by the live rock.
All this takes place in the first inch or two of sand, so it is not a deep bed that changes the dynamics, it is the presence of any sand. A deeper sand bed provides little additional benefit because the nitrite is consumed before it has a chance to diffuse any deeper.
Richard Harker