White layer is not normally tolerated on gears due to its brittle nature and high line contact loads to which many gears are subjected. There are exceptions. The benefit of nitriding gears is that extremely good dimensional control is possible because the gear is finish machined (with some allowance for growth during nitriding) and does not go through austenite transformation thereafter -- nitriding is done in the vicinity of 1000 F which is below the transformation temperature (at or above 1300 F). The benefit to most gears, as previously stated, is from the case that is formed, not from the white layer.
The white layer does have its benefits. I worked on an application where a shaft on which the spider gears of a differential ran steel on steel. Diametral clearance was critical, but without a white layer, seizure failure was assured. The white layer has an inherently low coefficient of friction, i.e. good lubricity, making it very beneficial when in a high speed but low load application.
The following is a brief and simplified explanation of the difference between the white layer, sometimes referred to as the compound layer and the nitrided case. The white layer is a boundary layer ranging between minimal to upward to .002" in thickness. Typical thicknesses are .0005 - .0015" when produced by conventional gas nitriding. It is called a compound layer because it is made up of a number of different iron alloy nitrides, FE2-3N (epsilon), Fe4N (gamma) being the more common. The white layer is formed by direct contact with the nitriding atmosphere and is where the ammonia dissociates into its component, the most important being nascent nitrogen, which reacts with the steel surface to form the white layer. Diffusion then occurs from the white layer into the steel. As the nitrogen content of the steel increases, reactions occur between certain alloying elements (e.g. Cr, Al) to form extremely hard nitrides. But more importantly, the nitrogen remains in solid solution in the steel. The nitrogen atom's much smaller size permits it to nest within the steel alloy atoms, strenghtening the surface thereby increasing its hardness dramatically.