Interesting! My guess is that:
A) Fast food places are in the business of solving the masses nutricional needs (low margins!), while other restaurants are more in the business of selling a special experience that you could do without (high margins!): Article mentioning lower margin breakfast foods.
B) Because of the above, people will go to a fast food place if it solves a need, like having breakfast, but you won't pay much more than you would for cereal at home, so breakfast has to be dirt cheap at this places. And it does seem to be the cheapest meal on the menu in terms of protein/dollar.
C) Now going back home for lunch is usually a pain, so they are able to extract a higher rent from you there, so they sell you fries and bread with some meat instead of a large meal of eggs and sausage. They make a larger margin on lunch items, so they have to shut the breakfast ones down. You are on a budget, so you'll go there again because its cheap, even if you are unhappy with them. If I was on a tight budget I would get the breakfast any time of the day if it were available.
D) Other places will sell you a breakfast any part of the day because they want you to be happy and come back, they make a big margin on anything they sell. Moreover, you'd be mad if they didn't have what you wanted, and you don't really need them. Plus who's gonna order eggs for lunch with their boss or with their boyfriend/girlfriend anyway? So even if the margins were lower, few people buy these items...