Why is that eggs have always been an integral part of the American (if not the Western) breakfast diet? When did this start and what was the root cause?
Chickens lay eggs mostly in the morning. So using them for breakfast is a natural consequence of having to go collect the eggs, and why eggs around the world are a breakfast staple, at least for people who keep chickens.
http://www.roysfarm.com/what-time-do-hens-lay-eggs/
Hens usually ovulate in the morning but can ovulate as late as 3 p.m. Ovulation occurs about an hour after laying an egg.
However it wasn't till the 1920's when factory farming of eggs made them ubiquitous in American marketplaces that a man named Edward L. Bernays launched a campaign -- he was a PR man -- to make bacon and eggs the American breakfast. He was working for a company that sold bacon at the time.
Here you can listen to him explain how the quintessential American-style bacon and eggs breakfast was invented and marketed.