It looks like the AAP recommends it because of the amount of cholesterol in the eggs less about the eggs themselves ETA so along as your aren’t concerned about their h cholesterol intake your fine.
We split a boiled egg everyday but I chop it and then heat it on the pan with tofu. So we eat about 3-4 eggs a week (total).
My son eats like 3 eggs almost everyday for breakfast along with sausage or something else😅
We do eggs about 4-5 times a week, too. She doesn’t always eat it all, but we’ve had no issues.