I've been wondering about this myself for some time, all the while eating cartons of egg whites for breakfast every day.
ericd posted a link[1], which appears to be a good source of information (far more than I have time to digest right now).
I only want to point out one small tidbit that I just found[2]; the American Heart Association (according to the webmd article) recommends keeping your dietary cholesterol intake below 300 milligrams per day. The same article reports that a chicken egg contains about 200 milligrams of it.
Now, I'm totally agnostic about things that I don't have time to properly research. In this case I would rather err on the side of caution, and will continue to limit my cholesterol intake.
That said, this app is nice if you enjoy eating this way (a bit of this and a bit of that; sans-recipe). This is pretty much how I normally eat, except that I never measure my portions.
A nice (premium?) feature might be a journal where you can easily record what you actually ate (in so much as it differs from the generated plan), your weight, etc.
I don't know, but maybe with enough journal data you could infer something about the user's metabolism (and average plan adherence), and make predictions about weight change.
1. http://www.ncbi.nlm.nih.gov/pubmed/21776466 2. http://www.webmd.com/food-recipes/features/cholesterol-food