Losing weight is simple -- just burn off more calories than you consume. What makes this difficult is that people try to reduce the "consumption" side of the equation instead of increasing the "burning" side.
Having said that, I can also see the value of an Atkins-type diet. I have found that carbohydrates tend to slow the body's metabolism, thereby making it harder to burn calories during periods of low activity.
Sure-fire way to lose a ton of weight -- get a full night's sleep every night, get up early, and exercise in the morning, even moderately. It will raise your body's metabolism for the entire day.
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.