Transmissions, steering gear boxes, and differentials need a specially designed lubricant that has the ability to "climb" the gears while rotating against each other. This "climbing" effect allows the lubricant to pass from one gear to the other, and so on while moving. The same principle is true with ball and roller bearings. The manufacturers knew this and specified and a gear lubricant to be at least in a semi-liquid state to do just that. If grease is used, the grease is squeezed out from between the teeth (or bearing surfaces) with nothing to replace it. Once the lube is gone, the heavy shearing loads against them doesn't take long for gears and bearings to rapidly wear themselves out.