Well, this is interesting.
Instead of looking for changes in nutrients, I tried to find what researchers and the USDA did research. Then I started finding more.
"Haugh unit" (pronounced how unit) is a measure of the albumen height. It turns out there are lots of factors that affect that besides storage time. Age of hen, strain of the hen (white eggs vary less than brown eggs) heat stress on the hens, whether they stop laying for a time, how quickly they are cooled and how to what temperature they are cooled, whether they are oiled, ...
Vitelline membrane becomes less elastic over time. Then customers get more broken yolks when they crack their eggs.
The study I found that concluded with, "...The results indicated that although the physical quality factors monitored in this study decreased during storage, egg quality was still acceptable beyond current recommended shelf life guidelines."
Ah, another study explained the veteline membrane is important because the yolk contains the nutrients needed for bacterial growth. If the veteline membrane isn't intact then the contents of the yolk diffuse into the whites with bad results. So, (my conclusion) is if you store an egg where it doesn't get jostled and leave it alone until you use it, you can safely store it longer than it you shift it around gently. And much longer than if you move it abruptly.
The pH inside the egg changes over time - no study yet that says so but that should affect how well various microbes can grow. If they did get past the bloom.
Edit to add
The yolk membrane elasticity decreases with the age of the hen also.