So I did some additional research this week to try and figure out why this diet works, and found an interesting article on the importance of Choline in liver function over on The Daily Lipid http://blog.cholesterol-and-health.com/2010/11/sweet-truth-about-liver-and-egg-yolks.html. It seems that egg yolks are extremely high in Choline, which as it turns out is critical to our liver being able to metabolize fat. In fact, when Choline is deficient (as it is in much of the modern US population), it can lead to Non Alcoholic Fatty Liver Disease – this means your poor, fat, lazy liver can’t even handle it’s own business – let alone helping rid the rest of your body of excess fat!
“…eggs are pretty much the perfect liver food.”
Also important to helping your liver metabolize fat are Casein (present in cheese and other dairy products) and an amino acid called Methionine. Guess what food has the highest amount of methionine in it? Egg whites! So between the massive amounts of Choline in the yolks, and the bounty of Methionine in the whites, eggs are pretty much the perfect liver food – add some Casein in the form of cheese, and you’re in business! And by the way, this trifecta of liver superstars are pretty much cancelled out in the presence of excess glucose from food or alcohol – which an egg fast also eliminates. Genius.{/quote]
Read more at http://www.ibreatheimhungry.com/2014/07/egg-fast-diet-menu-plan-low-carb-keto.html#uoAPjQaXcWRQcDg4.99

I'd been incorporating more eggs from the beginning, but this was nice information to know and encourages me to stick with my eggs.