It's tempting to view American education history as a straight line, concise and unwavering. But you're right, like most things, it's more complicated. Mann, and many others, did go to Prussia. And he was impressed, encouraged, and inspired by what he saw in schools. His main takeaway, generally speaking, according to his reports and letters, was that a centralized system was possible and doable. His (and others') goal for that system, however, wasn't soldiers or factory workers; it was meritocracy and citizenship.

Mann's advocacy for universal education for all (by which we're talking white children, mostly boys) was effective in that he was able to persuade northeast state leaders to support teacher training, build new schools, and hire more teachers. However, some areas of the country were already moving in that direction before he issued his reports. It's also slightly misleading to say the founding fathers were comfortable leaving education in the hands of religious schools - Jefferson especially was very vocal about his desire for universal, secular, classical (meaning the study of languages, math, and sciences) for all children (by which he meant white boys), regardless of class.

One of the patterns in the rise of the Common School movement that belays the "Prussian model" argument was who exactly Mann (and others) saw as the ideal teacher. For most the colonial era and the early 1800's, the average teacher was a white man (often married) who relied on corporal punishment and recitations to ensure his students, mostly adolescent boys from families of means, were compliant. By the early 1900's, the typical teacher was an unmarried white woman who taught groups of children of all ages and relied on routines and "feminine" skills to keep her charges in line and focused. American education leaders of the time saw young white women as the ideal teacher. She could shape young American minds, encourage free thought, and ensure future citizens were informed and literate.

To be sure, Prussia served as a bit of a touchstone for American educators throughout the rise of the Common School model but it was more about inspiration for the how of large-scale education than the what. An example of this is an 1891 report to the New York State Department of Education where the author basically does a compare and contrast between NYS schools and Prussian ones. ("They do this, we do that.") The author concludes,

Every impartial person must admit that Prussia secures in good results the full value of the money expended, and that New York does not.The methods in use in Prussia can not be adopted as a whole in New York. This is clear.

Generally speaking, Prussia inspired American educators to think big, advocate for all children (by which again, they meant white, non-disabled, mostly boys), and organize systems.

When it comes to content, there was a gradual sea change in American educational institutions away from a classical curriculum to English or modern courses of study over the 1800's. Rather than focusing on learning that was, in effect, useless - education was increasingly accessible to boys who weren't going to become lawyers and politicians, Latin wasn't essential knowledge for running a farm - it was shifting to practical knowledge like functional arithmetic, history, and sciences. By 1910 or so, curriculum was beginning to settle into what we think of as a liberal arts of education - a little bit of everything, spread over 10 or 12 years. When the National Education Association (NEA) pulled together representatives from educational organizations across the country in the form of the Committee of Ten in 1897, the structure of studying reading, writing, history, science, languages, physical education, arts, and music was becoming the norm. The Committees' reports codified the structure of 8 years plus 4 years and again advocated for a diverse, comprehensive education for the goal of graduating good citizens.

A decade or so later schoolmen, literally men who ran schools, were caught up in the fad of scientific management. Finding ways to be more effective and efficient became the norm and education was no different. Andrew Carnegie was among those who became enamoured with the idea of solving problems by breaking it down into measurable units and his foundation established the Carnegie Unit. This unit was a key piece in determining what it meant to be college-ready (colleges have been complaining about unready students since forever) and helped the idea of a high school class period become typical.

Finally, mostly due to the 10th Amendment, education is up to the states. The diffuse nature of American education has mostly meant fits and starts, different approaches, and marked differences between areas of the country. In 2021, we can get into how the federal law, No Child Left Behind, was an attempt to smooth out some of the differences between states. And in 2032, we can get into how the Common Core was an attempt by state education leaders to leverage federal law into smooth out the differences even further.