That diet sounds like Dr. Stillman's Quick Weight Loss Diet. It's a fine plan, but Dr. Stillman specified that it was
only to be followed for a short time, something like 2 weeks, IIRC.
I have to agree with Pengu1.
One thing you need to consider is whether you can eat nothing but meat and eggs for the rest of your life. I sure can't! In fact, after 3 days on the M&E Fast, I get nauseated at just the thought of another egg or bite of meat.
One of the things that happens when you follow Atkins by the book is that you learn how different foods affect you, and how many grams of carbs you can eat each day without gaining weight. No matter how you lose your weight, at some point in the future you will have to be able to maintain your new, lower weight. You won't learn that eating nothing except meat and eggs.
It seems that the body sometimes adapts to having a very low level of carbs. For people who have made that adaptation by staying very low carb for a long period of time, weight gain in inevitable if they ever increase their carb intake. Just something I've observed here over the years.