Are eggs with dark yolks more nutritious?

Quite a few people think that "the darker the yolk, the higher the nutritional value."

To conclude first, the color of the yolk has nothing to do with nutritional value.

Egg yolk color is determined by the amount of carotenoid pigments (orange-yellow to red) in chicken feed. (Contained in carrots, paprika, etc.)
Specific pigments include mainly lutein and zeaxanthin, which belong to xanthophylls, and a small amount of cryptoxanthin and β-carotene.

Chicken feed is generally based on corn, mixed with various grains and animal ingredients. If you add paprika or marigold to corn, it will turn orange-yellow.
In recent years, white eggs grown mainly on rice have also become popular. White eggs contain 8.1g of fat per 100g, which is 2g less than regular eggs, and are also lower in calories.
These eggs are used in omelets and desserts in fine dining restaurants.

*Iodine egg is a product name. Eggs laid by chickens fed a diet rich in seaweed.

Also, red eggs (akadama, chadama) are not necessarily more nutritious. The color of the eggs is determined by the breed of chicken. (*Whether it tastes good or not is a personal preference.)

Also, eggshell color does not reflect differences in taste or nutritional value.
Determined by the type of hen that laid the eggs.