Researchers who lived in African tribes that are _really_ following the "old ways" found that tribespeople followed all kinds of sleep schedules. Somebody was up at almost _all_ times, including the middle of the night.
This makes total sense: you want at least somebody to be awake at all times to raise the alarm if a pride of lions happens to wander close by.
By doing the "split day" you just switch to another fixed pattern.