One interesting natural experiment in diet and exercise was rationing in wartime Britain where the population ate less and exercised more (petrol was also rationed). The results were fairly impressive:
As a result of the balanced diet provided by rationing, children's health improved and on average they were taller and heavier than before the war.
The incidence of anaemia and tooth decay dropped - while the average age at which people died from natural causes increased, despite the stresses and strains of war.
The principles behind rationing sound surprisingly similar to today's health messages: reduced consumption of meat, fats and sugar and more of the sort of foods, such as vegetables, which provide essential vitamins and minerals.
this led to other health benefits:
A war-time regiment would also help reduce your risk of heart disease, Type 2 diabetes and high blood pressure, as well as cancers such as post-menopausal breast cancer, kidney and colon cancer.
The same outcome of rationing was seen in Australia:
The government feared that rationing would result in deterioration in health on the home front but, in fact, the outcome was positive. Rationing resulted in a decline in diet related problems like obesity, diabetes and heart disease.
So it is clear, that whether or not the wartime Commonwealth diet was optimal, there is a known population-level intervention that will result in better health outcomes: restriction of food.
Now, as a matter of public policy, I am clearly opposed to doing this in a coercive manner (but then I still see tobacco smoking as a personal choice). But it is clear that relatively simple diets can have surprisingly positive health benefits.