Feeding hard boiled eggs is not about increasing the protein level being fed, it is about increasing the quality of protein being fed.feeding eggs to our birds... at 12% protein, that wouldn't be worth it to me.
I don't have any problem believing that hard boiled eggs are 12% protein simply based on the fact that the albumen is all protein but it is also 88% water. When you subtract out the water, that leaves 12% protein.
https://www.healthline.com/nutrition/protein-in-egg