You presume that every one operates in essentially the same way. That is simply not true. I can tell you from experience that I was one fatso that ate like a bird for years without losing any weight. The primary thrust of Atkins tis that some people do have much different metabolic function. I beleive that most chronically obese people would benefit from Atkins, but that the diet is wrong for those who just want to lose a few pounds or get back to their early twenties weight. In my case I am 60 pounds lighter now (in my mid forties) than I was at 19.
I think the advantage of Atkins is that it kind of "preps" your body for weight loss by increasing your metabolism, reducing cravings, etc. But in the long run the result is the same -- burning more calories than you consume.