Great question! There's a couple of ways to answer it and I wrote a whole big answer addressing the bad history in the article. As soon as I finished, I realized I was indulging my frustration with that author and missing the point of your question. My sense is your question is less about that particular article and more about how we talk about education history. I'm happy, though, to answer follow-up questions or address specific points in that article. At the end of your question, you ask for a short text and I absolutely understand and sympathize. There's always something cognitively rewarding when we can narrow a big topic down to a single narrative or throughline. However, there is simply no way to do that and maintain good histographical practices in American education history, which is what Gray focuses on.

First, the educational experiences of children on the middle chunk of the North American continent varied wildly based on class, race, gender, disability status, geographical location, and era. An enslaved Black child's access to education was dramatically different than that of the daughter of a socially-connected white family in Boston. The role of school in the life of an Indigenous child from a Northeast tribe whose parents voluntarily enrolled them in an Indian Boarding School was different than the role of school for an Indigenous child from near the modern-day Mexico-United States border. It could be different for the eldest son and the youngest son in a wealthy New England family. An immigrant child from Italy in New York City in the early 1900s versus an immigrant child from Sweden in Minnesota. This means that whenever anyone writes about "children", they're ignoring - or minimizing - a whole bunch of history.

Second, much of this variety is because there is no one American education history. Which is to say, no. Schools weren't designed to do XYZ because first, "American schools" is a misnomer and second, there is no grand design or designer. Due to lawmakers' and courts' interpretation of the 10th Amendment, education is primarily left up to the states (there are some exceptions, especially as it relates to DoD schools, education on reservations or tribal lands, etc.) Every single state and territory has its own education history that is shaped by who colonized the land, their role in the Civil War, the speed at which they embraced the idea of tax-payer funded education, how they used laws to mandate attendance, and the degree to which those in positions of authority and power listen to those without power. The same holds true for nearly every country in the world.

That said, the author of that particular article is Dr. Peter Gray, a high-profile leader of what's known as the "unschooling" movement. Which is to say, he is not a historian (which he does acknowledge) and using (bad) history to advocate a particular argument. Your read of the piece is accurate and it is an unreliable text, history-wise. But what he's doing is fairly common - he's narrowing a complex, complicated history down to a single narrative so that he can advocate for a position he supports (more on that in a bit.)

Although he only mentions it explicitly a few times, he's relying on a trope known as the "factory-model" narrative. To borrow from the Wikipedia article I wrote on the topic:

Generally speaking... [this narrative is] typically used in the context of discussing what the author has identified as negative aspects of public (or government-funded) schools. As an example, the "factory model of schools are "designed to create docile subjects and factory workers'". The phrases are also used to incorrectly suggest the look of American education hasn't changed since the 19th century. Educational historians describe the phrase as misleading and an inaccurate representation of the development of American public education.

We see him do this in his piece, especially where he says, "Employers in industry saw schooling as a way to create better workers... To them, the most crucial lessons were punctuality, following directions, tolerance for long hours of tedious work..."

My first draft was basically 10,000 characters on how wrong just that one paragraph is, but just as an example of how using that narrative that schools did anything because employers wanted them to is wrong, grammar schools for most of the 18th century typically had two sessions: 6-8 weeks in the winter, 6-8 weeks in the summer, usually broken up into two 2-3 hour long chunks a day. Younger children typically went in the summer when they were more likely to have a woman teacher and arts and crafts were fairly common. Children often played games, learned songs, and did the things children want to do. Meanwhile, teachers didn't want bored children - anyone who has spent more than 10 minutes around groups of small children knows that bored children find ways to make their own entertainment. To be sure, this wasn't a universal norm in early schoolhouses, but it was common enough that it's misleading to suggest a "tolerance for long hours of tedious work" was a learning objective for most teachers. To say nothing of the fact few schools - if any - had indoor plumbing. Outdoor privies were also fairly uncommon near schoolhouses. Teachers didn't have "long hours" with children.

To put it another way, when I'm in conversation with people who believe schools work the way they do because that's what employers want, I bring up factory schools. Not schools that look like factories (because as I explain in the Wikipedia article, that's a misleading narrative), but literal schools inside factories. NYC schools went through a massive population explosion in the early 1900s and as a way to reach as many children as possible, some aid societies would hold classes inside, or near, factories. The children would finish a shift and meet with the teacher in the same building or the next building over. It doesn't always change minds but it does typically change the conversation and allow for more breathing room around the complexities of American education history.

You asked for recommendations and I'm going to link to a couple of my older answers that provide overviews but I want to make one more point through some of my favorite books. Articles like Gray enrage me as they, in effect, ignore the incredibly hard work of Black women in American education history in service to a narrative that benefits white, non-disabled cis, straight boys. If I was forced to narrow American education history down to a single narrative and could speak with very broad strokes, I would probably say it's been about white men in power doing what they can to ensure their sons inherit that power. We see evidence in the fact that despite the reality that girls have done better at school since the beginning of the common school movement, white men control most of the wealth and power in this country. In every generation, white fathers and mothers have used their power to advantage their sons. If we just look at modern education history, we can see how white parents in the South created segregation academics following Brown v. Board to ensure their daughters didn't have to sit next to Black boys at school. White parents created and moved to suburban enclaves following World War II while white parents who remained in the cities were instrumental in creating magnet schools. They pushed for secular homeschooling structures, taking advantage of carveouts created for religious objections to secular public schools. And now, they have advocates like Gray pushing for "unschooling", which positions public schools as something to be escaped.

Meanwhile, Black women - generation after generation - have fought for equitable access for their children. There were clandestine schools during slavery, often led by Black women who formed networks to share resources. Self-Taught by Heather Andrea Williams provides a solid overview of that history. In Pursuit of Knowledge: Black Women and Educational Activism in Antebellum America by Kabria Baumgartner is about the women who lobbied for changes to laws, built schools, protected girls from lynch mobs, and fought to get their daughters an education. And in The Lost Education of Horace Tate, Walker provides the reader with a deeper understanding of what individual teachers were doing around the time of Brown to ensure their students had what they needed for a rich, high-quality education.

None of that history is mentioned in Gray's piece. Part of understanding education history is siting with why an author might make that choice.

That said, here are a couple of pieces I've written that might be useful. There are more on my profile here.

• When did we start making kids sit down in school?
• Rise of tax-funded, compulsory education
• What did people think about the rise of public education?
• How true is the "factory-model"?
• Are schools about factory workers?
• "Production industry" and schools