If you were to set up a reef tank with high current, than there would be a lot of bare areas if you had a SB less than an inch high. 2-3 inches is the absolute best way to go. It would be incorrect to claim that a sand bed provides 'more capacity to nitrify and denitrify' simply because it's deeper.
"As much as 70 to 90 percent of the overall denitrification was located in the uppermost centimeter. The remainder was found at 1-3 cm depth"
-T.K. Anderson 1984 "Diurnal Variations of Nitrogen Cycling in Coastal, Marine Sediments."
"anaerobic habitat can be as small as 1mm, that aerobic and anaerobic bacteria essentially coexist, and that as little as 0.08mm distance is sufficient for nitrification and denitrification to take place simultaneously."
-Ecology and Evolution in Anoxic Worlds. Oxford University Press, Fenchel, T. and B.J. Finlay. 1995.
The misunderstanding is that areas with low levels of oxygen are a must for denitrification. Since we now know that aerobic and anaerobic bacteria exist together in the upper portion of the SB, than the heavy oxygen levels of our tanks would not be a factor. It's unlikely that denitrification will occur in the deep areas of a DSB, especially if nitrates never reach it in the first place.
I'd also like to point out that a deeper sand bed doesn't necesarily equate to more biodiversity of life. A shallow sand bed of numerous grain-size will create a number of different environments housing more life than a DSB.