I have an alternative answer to that question. Mammals evolved to sleep because those young that gave their parents a rest survived childhood. Seems obvious to any parent. :-) Imagine a puppy that never stopped. Its mother would abandon it.
The obvious advantages of not sleeping indicates to me that there is a deep connection between sleep and our waking performance. If there weren't why the hell would it have persisted across so many creatures for so long.
I am confused by the fact that human young keep parents awake so much: it seems like a delicate time to be introducing poor cognitive performance into the mix.
But then a lot of things confuse me when I apply straight forward darwinian thinking.
Since we can barely see in the dark and can't do anything anyway, wouldn't it be preferable to minimize the time spent defenseless against predators with better night vision? Staying still seems like a good strategy a lot of times, when most animal visions, night vision or not, is based on movement.
It doesn't answer, though, why the top of the food chain need to sleep too.
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.