How common is it for people to not have the concept of certain ‘breakfast food’?
In Japan the word for rice is gohan, breakfast is asa gohan, meaning "morning rice". Dinner is ban gohan. You get the idea - rice is the traditional part of every meal. 

Traditional Japanese breakfast food would be rice, fish, miso soup, vegetables, pickles. Which is a lot like a traditional lunch. More recently western breakfasts foods have been taken up some, so the concept of separate breakfast food is more of a thing.