Grocery is not heavily regulated, it's dominated by roughly 10 companies

But just because an industry is heavily dominated by a small number of corporations does not mean that there are no other choices. There are very few places I can think of where you don't have other options for your groceries besides going to SuperCorpMart. I don't see this as oligarchic, and it's certainly not monopolistic, like the current public school system.

In the context of education, a free market system might develop into a similar situation as the grocery retail industry, where a few major players dominate a large market share. But think about what that means. The biggest grocery chains presumably got to be the biggest grocery chains because they offer what the consumers want--in this case good product selection, low prices, pleasant customer experience, and close proximity to their homes. And yet, still, if a person does not want to shop at SuperCorpMart for their groceries, there are other options almost everywhere. There are mom and pop groceries, health food stores, farmers markets, online grocery ordering services, food pantries, and you always have the option of growing your own food. I'm not seeing how it would be a bad thing if the education market looked like the grocery retail market.

Cellular service is not heavily regulated, it's dominated by 4 companies

What country do you live in? In the United States, cellular service is heavily regulated by the FCC.

Powerful companies create regulation so they can dominate or control an industry.

Agreed. This is one reason why I'm an anarchist. If there was no vehicle for market compulsion, this would be near impossible to achieve.

The "we" I refer to is society as a whole. If you do not want to be included in that "we" that's fine.

I understand that you're referring to society as a whole. My point by saying "there is no we" is to show that, in most cases, and in all economically concerned cases, there is no such thing as "what is best for all of us." You have your opinion--that children should be taught using the scientific method as a foundation. Other people might think that it is best for them to learn an arts-centered curriculum. Others might value bilingual education above all else, and others might consider religious education as the most important foundation. There is no "we" because we don't all want the same things, and trying to convince all of society that your idea is best is going to be a never-ending pissing match. That's why the only thing that can be best for "we" is to let each individual make the choice for themselves.