Go read Steven Pinker or Daniel Dennett or someone with something intelligent to say on this topic.
If I recall correctly, their argument is that you are asking the wrong question: Not why do we sleep, but why are we ever awake? Why do you assume that being awake is a desirable thing from the gene's point of view?
Sleeping conserves energy, reduces the chances of harmful accidents, etc. All things that help the gene's chance of staying incarnate. When there is nothing better to do, i.e. after you have fed, mated and found a spot safe from predators, what is so bizarre about conserving energy by not doing much for a while?
sleep reduces the time available to reproduce Since when has lack of time to shag been the limiting factor? It doesn't take that long. Pregnancy takes months for most species, how does sleeping reduce the time available to do this?
it opens us up to much more danger from predators Does it? Which is more likely to get you spotted by a predator: hiding in a cave and not moving, or roaming the countryside.