It is important first to unpack an assumption in your question, which seems to consider as "traditional" breakfast what is now traditional in the United States. Eggs, bacon and pancakes are not considered traditional breakfast everywhere, and I would guess not even in the majority of places. I am not north-american nor a historian but I have read a bit in this topic so I'll leave the mods to decide if this answer is good enough.
Some of the very early breakfast options in the US were mainly grain-based foods such as corn, a staple from indigenous people's diet, oat, wheat and barley. For example, North American indians would make what would be later called "grits" from ground corn. However, breakfast was not always a popular meal at all, and its introduction and popularity in the US could be traced back to the colonists and pilgrims. There's a reason for the whole Quaker and oatmeal imagery in products. It was indeed at the origins of breakfast in the US, and at the same time the United States were being "born", the breakfast as a daily meal was at a comeback period.
Throughout most of the middle ages, breakfast was frowned upon and mostly seen as something only peasants had to resort to, since they needed the extra energy to go about their daily heavy workload. Children and the elderly were also tolerated for similar reasons. The Church frowned upon it and saw breakfast associated to overindulgence and gluttony, described by Aquinas in his Summa Theologica as praepropere, the sin of eating too soon.
In the book Breakfast: A History, by Heather Arndt Anderson, she argues that the "golden age of breakfast" was in the 17th century. This perhaps coincides with the golden period of Dutch paitings, including many breakfast-themed still-lifes from the period. This is also heavily influenced by trade: Europe at the time is receiving a lot of stuff like tea, coffee and chocolate from elsewhere and the wealthy are incorporating this in their diets. This was so prevalent that it sparked some religious debate over whether chocolate, for example, would break one's fasting or not.
From Pope Gregory XVFs Chocolate Enterprise: How Some Italian Clerics Survived Financially
During the Napoleonic Era by Christopher Korten:
So quickly had the consumption of chocolate grown in Italian lands that by the middle of seventeenth century a determination had to be made whether or not this practice violated Church fasts. Did chocolate offer the requisite “nourishment and sensual satisfaction,” to be considered food? In 1662 Cardinal Francesco Maria Brancaccio judged that it did not: “Liquidum non frangit jejunum” or “Liquids do not break the fast” was his oft-quoted response. Even earlier, in 1569, Pope Paul V declared that the consumption of chocolate during lent in New Spain was permissible. This decision followed an appeal by the bishop of Mexico, who witnessed alarming levels of consumption by those in his diocese. It was rumored that following Paul V’s first taste of the (presumably unsweetened) drink, he was so disgusted that he believed that it in no way disturbed the fast.
Despite Paul’s initial revulsion, privileged churchmen as well as Roman aristocracy quickly began including chocolate in their breakfast routine.
The same Dutch seem to have a lot of influence in American breakfast. Waffles, traditionally Dutch, were also introduced by pilgrims of dutch descent. They also ate a lot of corn and oat, as mentioned previously, and that, along with the indigenous grit, estabilished cooked cereals as a staple in north american breakfast, which would be transformed in the 19th century with the invention of ready-to-eat, cold cereal. In North America in general, there was also the use of maple syrup from indigenous people before any colonists.
Now, regarding breakfast in the United States as we know today, as you call it the "traditional", Edward Bernays (1891 - 1995), "the father of public relations" and Freud's nephew, is considered the one responsible for popularising bacon and eggs as breakfast options. These were certainly possible elements of a breakfast before him, but were not what you would call traditional. Meat and eggs were part of european breakfast since it started to become a socially "acceptable" meal, especially in France and England, but not so popular in the US, where the most common were grains and cooked cereals, bread, coffee and juice.
The reason why meat was not so popular in breakfast at the time is the Clean Living Movement, a period of moral health reforms in America. According to Angels and Vegetables: A Brief History of Food Advice in America by Melanie Du Puis, there was a strong food reforming movement advocating for reduction of meat consumption closely linked to religious principles:
Americans ate so much meat that indigestion and constipation were near-constant worries, with enema bags and mercury pills a daily form of relief for many. The relationship between the physical and national pathologies seemed evident: slavery was like an impassible bolus bringing sickness to the national system, just as meat clogged the body. Meat and slavery became intrinsically bound, and reformers sought to abolish both by linking vegetarianism and abolition.
One famous religious reformer was Sylvester Graham. From the same source as previous:
Rochester, New York, had become the country’s first boomtown following the completion of the Erie Canal. Only a few blocks away from the Rochester Presbyterian church where Finney preached stood the city’s flourmills, including one that produced the graham flour invented by Sylvester Graham. Like Finney, Graham was an ordained minister in the Presbyterian Church and an itinerant proselytizer, but he preached the salvation of health reform. Where Finney sought to replace predestination with the idea that humans could perfect themselves and their world, Graham preached the creation of a perfected life through abstention from the evils of meat, spices, fat, and sex (especially the so-called solitary vice). His invention of the
graham cracker was meant to deliver the public from the evils of white bread.
Grahamism would later influence people like Kellogs in developing corn cereals that were more easily consumed, with no need for cooking.
Anyways, back to Bernays, he was a pioneer of public relations and propaganda, applying his uncle Freud's theories on the human mind and desire, in order to sell products and shape consumer behaviour. This is extensively covered in Adam Curtis' documentary The Century of the Self. Bernays was approached by the Beech-Nut Packing Company in the 1920's to make bacon more marketable and increase demand. Bernays then consulted with doctors and published in newspapers their opinions on the matter, pointing to advantages of a "heavier" breakfast of bacon and eggs. Here is a video of Bernays himself explaining this process. This is how bacon, specifically, became a staple of american breakfast, and how America moved away from the previously traditional light breakfasts toward something "heavier" in the early 20th century.
edit: u/lord_mayor_of_reddit convincingly pointed out that Bernays' role in popularizing bacon and eggs is vastly overstated. Bacon already could be considered traditional prior to that, Bernays just ran a successful marketing campaign that boosted its sales and re-claimed its position as a "healthy" breakfast option, which had been shaken since the health reforms of the 19th century.
So, /u/Boeotian_ did a great job talking about the origins of breakfast as a meal, but didn't really cover why those particular foods. As he mentioned, breakfast was seen as a "peasant" meal because it was favored by people who needed a lot of calories before a long hard day of labor. We currently live in an era of unprecedented food convenience, and so it can be hard to imagine living in a world where just about every meal was a home made meal and required a trek out to the local mill, dairy, bakery or butcher. Most homes before the 1850's would not have had ice boxes or methods to easily refrigerate foods. Before freezing and refrigeration, people had to use preservation methods like pickling, curing, fermenting, drying, jarring, and salting etc. You might be able to keep things like fruit preserves (jams and jellies), salted, cured or dried meat (like sausages or bacon), cheeses, and grains. However, the longer foodstuffs were kept in the house, the more likely that they would see spoilage or be eaten by pests like mice, rats and weevils. So, every day that a person went out to make their own food would require picking up a lot of ingredients fresh from local businesses, or labor to harvest it from resources owned by the household like a garden or livestock.
Breakfast, kind of by definition, is a meal that comes before the daily tasks involved in maintaining a household or doing labor. So, breakfast foods for a peasant household would be foods that were already "on hand" or able to be made relatively quickly. Getting fresh meat might require checking traps and skinning and butchering an animal, or a trip out to the local butcher's to purchase pre-portioned meat. Cooking it over a fire could take an hour. Or, you could take whatever leftover grain and flour from the previous day is still in the grain ark and make some pancakes in about 15 minutes. Eggs can be gathered in a matter of ten minutes or so if one has their own birds like chickens, ducks or geese, and cooked in a matter of a couple minutes. Cured meats and cheeses would be ready to eat either heated or at room temp, didn't require refrigeration and could be bought beforehand and stored for a few days. Toasting could help reinvigorate bread bought or made the day before that had gone stale, and then topped with fruit preserves. Completely stale bread could be soaked in egg and fried to make French toast. Porridge or pottage could be food that was cooked the night before for dinner and left over the fire to be eaten in the morning. Since the merit of these foods is that they're quick to prepare, high in calories, and easy to store in your house, it's no surprise that they were widely eaten in Western society by the working class.
Some great information can be found in Breakfast: a History by Heather Anderson
Before cereal, in the mid 1800s, the American breakfast was not all that different from other meals. Middle- and upper-class Americans ate eggs, pastries, and pancakes, but also oysters, boiled chickens, and beef steaks.
In the days before home freezers and rapid transit, suggested family menus were grouped by season and presented for each day. Breakfast would have been served between 8-9AM. Dinner would have been the main meal of the day, served sometime between noon and three. Tea would have been a light meal (at that time this meal was often called supper) before retiring.
Bill of Fare - Winter:
Monday. Breakfast - Corn bread, cold bread, stew, boiled eggs. Dinner - Soup, cold joint, calves' head, vegetables. Dessert - Puddings, &c. Tea. Cold bread, milk toast, stewed fruit.
Tuesday. Breakfast - Hot cakes, cold bread, sausages, fried potatoes. Dinner - Soup, roast turkey, cranberry sauce, boiled ham, vegetables. Dessert - Pie &c. Tea. Corn bread, cold bread, stewed oysters.
Wednesday. Breakfast - Hot bread, cold bread, chops, omelet. Dinner - Boiled mutton, stewed liver, vegetables. Dessert - Pudding, &c. Tea. Hot light bread, cold bread, fish, stewed fruit.
Thursday. Breakfast - Hot cakes, cold bread, sausages, fried potatoes. Dinner - Soup, poultry, cutlets, vegetables. Dessert - Custards and stewed fruit. Tea. Corn bread, cold bread, frizzled beef, stewed fruits, or soused calves' feet.
Friday. Breakfast - Hot bread, cold bread, chops, omelet. Dinner - Soup, fish, roast mutton and currant jelly, vegetables. Dessert - Pudding, &c. Tea. Hot light bread, cold bread, stewed fruit.
Saturday. Breakfast - Hot bread, a nice hash, fried potatoes. Dinner - Soup, roast veal, steaks, oyster pie, vegetables. Dessert - Custards. Tea. Corn bread, cold bread, stewed oysters.
Sunday. Breakfast - Cold bread, croquets, omelet. Dinner - Roast pig, apple sauce, steaks, vegetables. Dessert - Pie, jelly. Tea. Cold bread, stewed fruit, light cake
SOUPS
pepper pot, pea, clam (broth and with cream), oyster, beef, veal or mutton broth (with vegetables)
BREADS
corn bread, potato bread, muffins (wheat, fruit), rusk, sally lunn
MEAT, FOWL & FISH
roasts (beef, mutton, pork), ham, turkey, venison, goose, duck, cod, halibut, shad, mackerel
MADE DISHES
meat & vegetables pies, stew, hash, veal cutlets, rare bit, beef alamode
VEGETABLES (Note: some of these would have been difficult to obtain in the early parts of the century, but by the middle 1800's, they would have been fairly common):
succotash, boiled onions (with cream sauce), spinach (with hard boiled egg slices on top), potatoes (boiled, fricasseed), corn pudding, peas (with butter), boiled cauliflower, stewed carrots.
DESSERT
fruit pies, cheesecake, puddings (these were the steamed British type, as in plum pudding), custards & creams (lemon, orange), spice cakes, sugar cookies, ice cream. NO CHOCOLATE.
BEVERAGES
hot chocolate, coffee, tea, fruit wines and cordials, ale, shrub, Madeira, and rum.
Did you also know that Dinner and Supper are totally 2 different things. Back in the 1800's a lot of people ate 4 meals a day compared to the 3 modern meals we eat today. Back in the 1800's the meals consisted of.
Breakfast. Usually ate around 3-5 in the morning before going to work and wouls consist of either oatmeal and bread, porridge and bread, eggs, bacon, milk or orange juice, cream of wheat, grits, corn, or cereal but cereal became a huge staple after James Caleb Jackson invented the first dry whole grain breakfast cereal. Cereal was originally invented to help cure cure intemperance and masturbation.
Lunch was non existent in the 1800's in the United States but some people would eat a snack or fruit
Dinner. Was usually eaten around 1 to 3
Tea. From 6 to 8
Supper. Typically eaten around six to eight. syrup-water or lemonade and cakes, unless wines are used; or ice-cream and ice-water, if desired; and sponge-cake, or lady-cake, or small wine cake, or any other not too rich, which may be preferred. Capillaire or orgeat may be used to flavor a tumbler of ice-water, instead of syrup or lemonade."
Lunch didn't really become popular in the United States until the early 1900's.