I study history as a hobby (been studying nutrition for a few days, only) and the way that the "Paleo hunter-gatherer" is theoretically described seems reminiscent to the lifestyle of ancient Arabs (200-800 AD). Insomuchas, fairly natural things were consumed, meals hard to come by, etc.
A typical way to eat dates (for the morning meal especially, but also for the evening meal) was to dip them in a paste made from ghee and fried ground millet. Dates are dense (filling) and based on what I've read, millet is filling. So, perhaps this combination got them through the day quite well, when a third meal was the exception, not the rule.
Dates, either alone, or in combinations like this, were a staple of the ancient Middle East, and people subsisted on them for meals at a time.
Dates can be stored for up to a year (hence, were often bought in year-long supplies at harvest-time, by those with the capital to do so), can be easily transported, do not damage easily, and are filling. The cultivation process is labor-intensive, and makes them more expensive than other fruits, like bananas. There are many varieties, not all of them are soft and melty. Most of the bedouins would have subsisted on harder, dryer kinds. Many would have eaten hardened dates, long before, or long past their ideal eating time.
I don't know about their nutritional benefits, outside of the basic stuff that can be gleaned from Google, but at least some groups throughout history, leading lifestyles reminiscent of hunters and gatherers, relied on them heavily.