The Okinawan sweet potato diet thing was caused by the post-war devastation to the island such that only the easiest to grow foods were available. It indicates more that calorie restriction and fasting (involuntary in this case) caused the longevity. The newer generations do not eat that same diet.
Because the type of fasting this sub promotes is basically crash dieting, and most people are just trying to avoid sugar and carbs.
Also I don’t think you are on the money with the low protein hypothesis. If a greater part of their diet is veggies etc, they are burning more calories consuming their food and getting fewer total calories. That is where the longevity element comes in. You body needs proteins for most of the cool things it wants to do, and the higher mortality rate in places like America come from overconsumption not just dietary balance.
That’s the claim in the Jason Fung fasting material. Some of my family members have eaten a carbohydrate and fat only diet, but it was the war and everyone was hungry. The fat was there to slow down digestion and keep you full longer. Not sure how practical that is today when there’s no actual food shortage. I’d probably overeat if I tried it, i’d just fast a few days instead.