The reason low carb diets lead to weight loss is because they restrict calories. I'm aware of many dieting tricks that can assist, but a calorie deficit must be created in order for weight to be lost.

No one in this thread is disputing that you need a calorie deficit to lose weight. My contention is that this is merely the beginning, not the end. Let's refer to the following passage from the linked article:

Translation of our results to real-world weight-loss diets for treatment of obesity is limited since the experimental design and model simulations relied on strict control of food intake, which is unrealistic in free-living individuals.

A diet should be realistic for free-living individuals. An obese person who wants to lose 50+ lb. could expect to be at it for the better part of a year. A diet that leaves you hungry all day is doomed to fail: it's unrealistic to expect pure willpower to last that long. That is the point of my post about hunger control. Disregarding it or dismissing it as a mere trick is to ignore that a very important part of dieting is making sure the dieter sticks to the diet.

My point was to specifically disparage diets like the Atkins Diet. It does nothing apart from restricting calories, yet libraries have been written about the magic of how and why it works. It's all just noise aimed at selling books, etc. to people who are looking for help.

Quite the contrary. The Atkins Diet is not just about losing the weight. It also includes a plan to keep it off. Maintaining weight loss is generally harder than losing the weight in the first place. Yo-yo dieting) is a very real problem. The problem with naive calorie restriction is that it doesn't instill good eating habits that can be maintained once the weight-loss period ends. The Atkins Diet addresses this and is designed to ease one into eating habits that will maintain the weight loss.