Toothed whales (incl. dolphins) can apparently sleep with just half their brain at a time, while remaining alert with the other half.
Thus, there exists a solution in nature wherein the creature experiences the benefits of both regular sleep and continuous alertness. The rarity of the solution suggests that sleep is more important for most mammals, except in niches where a prolonged loss of consciousness could lead to drowning, or being eaten by sharks.
Also recall that as social, tribal animals, modern humans relied on aunts and grandmothers to relieve exhausted mothers for all of prehistory. Separate homes for smaller family units and wider geographic dispersal of family members are relatively recent developments. I wouldn't expect biological adaptations to the practice to appear any time soon. I think the most likely event is that we will discover and use a pharmaceutical remedy for sleep deprivation in parents, possibly by studying dolphin brains.