Why are there not more competitive nonprofits? For example, when I go to the grocery, and peruse the various goods for sale on the shelves, there is at least a 99.9% chance that any given product is produced for-profit.  Even "Newman's Own", which gives all of it's profits to charity, is classified as being for-profit.

Why are there no non-profit brands of, e.g. breakfast cereal, whose goal is to simply provide consumers with a healthy and affordable morning meal, but not to make a profit?
There is a Hungarian economist by the name János Kornai, who has renowned work on eastern block socialist systems. He has devised a system theory on coordination mechanisms which guide the way people work together and allocate resources. Based on this theory you can explain different economic and political systems as well. The four coordination mechanisms are:


market (for-profit business - capitalism)
bureaucratic (the state - socialism)
ethical (non-profit, charity organizations, the church etc.)
aggressive (organized crime etc.)


From these four, the ethical is the mechanism which guides charity and non-profit organizations, which is actually the weakest in terms of efficiency. The guiding objectives are grounded on moral and altruistic behavior, but as humans are collectively more selfish in reality, this does not work too well. There is a crowding-out process, by which market coordination takes over in that certain field. Which is in your case the FMCG industry. Even if there are some moral initiatives to simply provide consumers with a healthy and affordable morning meal, but not to make a profit, slowly the enthusiasm erodes and people start to behave more selfish, and exploit the the brand and image to make money. Look at part III. section 1. of the article titled, Neither bureaucracy, nor market? for a good explanation.