Lilah eats an egg almost every morning. She loves it, and then I know she's eaten at least some protein and good fats early in the day. Eggs are loaded with all kinds of nutritious goodies, including iron and folate, as well as protein. And young children actually need cholesterol in their diets to provide the building blocks for myelin development (myelin is a substance that coats the neurons), which is why parents of vegan children are advised to breastfeed to at least two years of age-- since the vegan diet doesn't provide any cholesterol, breastmilk is the only way a child will get it. I also find eggs to be handy ways to get veggies into a child-- frittatas and omelettes are really good vehicles for those.
Anyway, I am a big fan of eggs myself, and while I don't eat one every day, I don't fret about the weeks that I might eat more than one per day.