Well, try an experiment. Find a time of day when you are alert and well-rested, and lay still in your bed with no external entertainment for eight hours

I'm not saying the idea is correct, but your argument is sorely lacking in plausibility - creatures with complex nervous systems get bored staying still unless they lose consciousness (and actually, we spend a lot of sleep with our brains still active in dream-world). If evolution "wanted" to come up with a way to keep animals out of trouble for the part of the day they'd be vulnerable, sleep might be a reasonable and generic way of doing so