Why worker sterility? Kin selection
Because of haplodiploidy, workers are more closely related to sisters (r = 3/4) than to offspring (r = 1/2), assuming females mate once
But, they are more closely related to male offspring (r = 1/2) and nephews (r = 3/8) than to brothers (r = 1/4). Therefore, workers should lay unfertilized eggs if mothers mate singly (bumblebees, stingless bees)
If mothers are polyandrous, then female workers may be more closely related to brothers than half-nephews (r = 1/8). Expect workers to kill unfertilized eggs laid by other workers in polyandrous species, e.g. honeybees.