That's just it: you CAN'T eat that many calories on a meat-rich diet. After a week of following Atkins' induction plan, your appetite starts to drop off dramatically. You don't really want to eat much.
And having all of that protein means you won't burn any lean muscle tissue when you being to burn through your fat stores.
Precisely, which is the real trick of all this.
I capitalize on this by eating a carefully engineered breakfast that keeps me fully sated until around dinner time when I come home from work. It is a pint and a half of a low-carb concoction I engineered that only contains about 700 calories but keeps me from feeling hungry for 8-12 hours and several cups of coffee. Ironically, it is a minor variation on a concoction I used to love and eat all the time anyway. It also allows me to spend less time at work, since I skip lunch. A normal dinner (veggies and fish or lean meat typically, but with no effort to reduce fat), and I'm done for the day. All upside, no downside.
I'm not really in need of a diet (I'm relatively lean and muscular), but meat and veggie diets have me eating far less (no desire to snack) and keep me feeling much better and more even throughout the day. I eat far less now that my diet is virtually devoid of refined carbs, and having been eating like this for a year or two, I've also lost the desire to eat refined carbs (I feel like crap if I do eat them). Once you fully adapt to lean protein and veggies, it becomes as easy and habitual as any other diet.