CatVersusRoomba
1) Autolysis includes using up your body fat, so this doesn't contradict fasting for weight loss.
2) Detox. I've never seen any scientific evidence of what this even means. Various organs in our bodies are "detoxing" us all the time, whether that's the liver, the skin, the kidneys, whatever. You don't have to fast to "detox."
3) Destroy urges for caffeine, sugar, etc.
I think this works for some people as long as they are fasting. Since you can't fast forever, many people go back to their trigger foods/chemicals. Once the taste buds are awakened, it can be easy to revert back to using again. People kick these things without fasting, too.
I'm guessing historically fasting had nothing to do with any of these three - it was largely spiritual.