OK, this is something I know alot alot alot about. It was one of my Ph.D. exam questions. In archaeology, it is called the "Neolithic question" -- something we see over and over again in the skeletal remains of neolithic peoples. They are really unhealthy compared to their palaeolithic counterparts. Take one population which I know well -- Greece.
Remember: Palaeolithic = pre-agriculture. No dairy at all, hunting and gathering, wild meat. nomadic AND settled homes (caves) 500,000 BC until about 10,000 BC
Neolithic: agriculture, animals raised for meat/fur/dairy, settled villages as well as pastured areas away from the villages for their animals. After 10,000 BC (in the NE, 7,000 BC in Greece, later in Europe, Asia)
I've done alot of research on what people ate during both periods... Palaeolithic cultures DID eat grains and beans...not in the amount we do, to be sure, but they ate grasses and wild wheat/einkorn seasonally. They couldn't store them, but they did eat them when they were available in their areas. In Greece, there are 2 natural "harvests". The Near East, 3 harvests in some areas (the fertile crescent, where agriculture seems to have begun, is aptly named for this reason!) They ate lots of small wild game (small mammals that were probably shared with a large extended family by making broths or soups), rare large game, and alot of fish & birds -- in Greece, even deep sea tuna (which required pretty good boats...seagoing...in the PALAEOLITHIC period!) They ate lots of greens (lots), berries, fruit, wild olives, eggs. Basically, they ate whatever they could get their hands on. We find that they cooked some of their food, especially meat and grains/legumes. But, most was consumed raw.
The NEOLITHIC period, well , their diets are alot like ours. All of a sudden, people have terrible teeth, cancers, diabetes (you can tell all this from the bones), osteoporosis, arthritis, etc. etc. People were shorter, had shorter life spans, had trouble giving birth (more infant/maternal mortality.) The Neolithic marks the time period when people consuming diets of grain, beer, legumes, some meat (raised, not wild) and dairy products. All cooked and processed. All of which are great sources of calories, but really was a blow to people's health.
We know all of this for the palaeolithic period because we've EXCAVATED and recovered this evidence. It is possible (actually easy) to recover all this information for very ancient times. Some goes for the Neolithic period, but also in the Neolithic, we have written records (especially in the NE) that give us a description of what they are eating, records of eating/farming/animal husbandry, etc.
I have to agree--- our genetics dictate that the Palaeolithic way of eating is the way our biology (all of us) are supposed to eat. We became genetically human at the dawn of the palaeolithic period. Homo sapiens sapiens. We are the same people now as we were at the beginning of the palaeolithic period -- genetically, brain size, smarts, emotionally...language, sentimentality, art...we had it all by the time the palaeolithic period started. We have not adapted physically (genetically) to the influx of calories (with less nutritional value) that the neolithic/agricultural way of eating provides for us. This is a very very recent invention (Palaeolithic period begins 500,000 yrs ago in the NE. Compare that to the c. 10,000 yrs ago for the inception of agriculture.) People's health deteriorated in the Neolithic because of this. I am trying (badly most days, but trying) to eat with the palaeolithic diet in mind. Small amounts of grain/legumes, large amounts of veggies, fish, broths (not from small mammals, but chicken...) berries, fruits, eggs....AS SEASONALLY AS POSSIBLE! As raw as possible.
OK, sorry for the rant, but this is (archaeologically) an area of interest of mine. Just thought I'd share.