What's With All the Different Colors of Bird's Eggs?

Distinctive American Robin eggs in the nest

I remember as a child coming across broken blue eggshells in my suburban wanderings. They looked like tiny Easter eggs. My father told me they were from a robin's nest. Amazing. My mother would sometimes buy eggs from the store that were brown instead of white. Different kinds of chicken, she told me. Did they taste different in my omelet? No. S then why do bird eggs come in different colors?

It was a mystery to me and my parents and it turns out that it is still a bit of a mystery. My childhood guesses would have been that it was so birds could tell each others eggs apart. Since it varies by species, I thought maybe it was "in their genes" like different colored eyes or hair in humans. But robin eggs are always that blue (as far as I can find) so it's not some variation by the individual.

Some research on tropical birds had shown that darker hues help guard against predation because they were better camouflaged. They also found that deep pigments in eggshells also contain light-activated molecules that protect against infections. Then why would any bird evolve to have light-colored eggs?

Some new research suggests that birds up north lay dark eggs because those colors help keep the growing chick warm.

Variations of Grey Butcher Bird eggs

But then wouldn't birds in hotter climates with dark eggs run a higher risk of making the egg too hot.?

Eggs have to stay around 90 degrees Fahrenheit to hatch. I learned through some volunteer work with beach-nesting birds that one reason the birds need to sit on them constantly is not to keep them warm but to offer protection from the sun. If internal temperatures get too high, the egg cooks.

Researchers mapping egg color data from 634 found increasingly darker eggs toward the highest latitudes, where sunlight becomes more scarce. For the birds with darker colors in hot and humid regions, predation and disease were more important reasons for dark colors.

What about the robin's egg blue? Surely, that bright blue color is not helping hide the egg. It seems like an attractor. Is it just that this particular shade is the right color for the heat control that robins need in their range? That seems to be the current thinking, but I'm not completely convinced.

Look at those eggs from the Grey Butcher Bird shown here. Why is there that rusty band on one end? Why not all one uniform color?  Camouflage? Not in that nest background.

Still a mystery.