I agree with you that eggs are very important sources of amino acids, energy and also some essential trace elements and vitamins.
Recently, we finished some dose : response studies with various Iodine supply in laying hens and found interesting results, which may be also very helpful to contribute to overcome Iodine-deficiency in many countries.
Attached, you will find a review of these studies. E.g. Table 7 demonstrates that one egg of hens fed with adequate I-supply may cover about 50% of the human Iodine-requirements.
Prof. Dr. G. Flachowsky
Senior Visiting Scientist
Institute of Animal Nutrition
Federal Research Institute of Animal Health