I think most people chose CD for the VLCD plan because it's an abstinence diet...as in no food
If you go to the higher plans, they have been formulated to be nutritionally balanced. Eggs (though lubberly) are high fat, so would probably make the proportion of fat too high. After all, if it was just about carbs, you might as well have a couple of eggs and fry them in olive oil. Zilch carbs.
My advice for what it's worth, is stick to the book. Start adding your own little variations and you may find things go off course