I had the same reaction as the mod who added the "great question" flair. When I got a heads up about your question, I immediately thought, "you know, I wonder about that, too!" So, I went to my largest, most comprehensive book on the history of American education and flipped to the index, looking for board, schools or schoolboards. Nadda. So I tried governance. No joy. Went to my second thickest book on American education, thinking perhaps the first author just avoided the topic. Nadda. Then I tried my trusty Historical Dictionary of American Education and again, nothing. (Though I did chuckle at the school choice, see vouchers entry.) Had there been an entry, I suspect it would have been school boards, see 10th Amendment, complicated.

The straightforward answer is that school boards aren't actually that powerful in America. Rather, there are states and school districts where school boards are incredibly powerful and states and school districts where they are not. The reason for that is our lack of a national education system. This means, in effect, at least 66 different governance structures (50 states, 14 territories, Department of Defense schools, Bureau of Indian Affairs schools.) Various outlets are fond of saying that Massachusetts had the first board of education in 1837 but my pedantic nature is such I must insist that New York State was actually first with the founding of the Board of Regents in 1784. Regardless, the basic idea behind both boards - and the modern school board - is that communities are best served when the community has a say in how its educational institutions are runs, and the best way to accomplish that is through elected representatives. This concept is generally described as, "local control." (However, there are some places where school board members are not directly elected and are instead, appointed by elected officials. Generally speaking, though, the people who sit on a school board are there because of one election or another.)

Despite my best efforts to identify a particular pattern and summarize the history, I kept getting stymied by exceptions - which is likely the reason the authors of the books I mentioned above didn't address the topic; there are just too many differences between states. For example, Texas has a fairly strong state-level board of education that limits some local control - the state mandates which textbooks teachers should use - but Texas school boards wield a fair amount of control over budgets, etc. New York State's board oversees all education in the state but does not, and cannot due to statute, force districts' hands around curriculum decisions but does set conditions around graduation. That said, school boards across the country typically have statements like, "All powers and duties not specifically delegated by statute to the STATE Education Agency or the STATE Board of Education are reserved for the board." or "In all cases where laws or regulations of the State Commissioner of Education do not provide, permit, or prohibit, the Board shall consider itself the agent responsible for establishing and appraising educational matters and activities." In other words, individual local school boards look to various state-level policy mandates to understand what's under their control.

One bit of history that's worth bringing in is the history around consolidation. From around the 1910s to the 1970s or so, the states went from over 100,000 schoolhouses to 13,000 school districts. During the rise of the common school movement in the mid-1800s, communities would build a school, staff it with a young, unmarried, likely white woman and figure out ways to fund it through a combination of taxes, state-level funding, and occasionally tuition. Sometimes these decisions were made by one person who was in charge of all of the schools in a particular country, in others, it was a formal school board that was elected alongside other community leaders. Over time, this settled into a system of property taxes and as transportation options expanded, communities realized they couldn't, or didn't have to - support several and sometimes dozens of schoolhouses in the same small area. WPA projects during the depression resulted in the construction of hundreds of large, regional high schools across the countries, functionally ending the era of the local schoolhouse.

During this same period, American schools saw the rise of "schoolmen." What we think of today as school administrators, "schoolmen" were a class of educators who sat between the teacher and the structure overseeing the running of the school. So, in a community where previously a school teacher reported directly to a small board, the increasing popularity of "schoolmen" meant there was now more likely to be a principal, and/or superintendent between the teacher and the community, represented by a school board. (To be sure, a whole bunch of this was shaped by sexism. There was a very strong paternalistic nature to the rise of schoolmen - I get into that a bit more here if you're interested.) As schools consolidated, the teacher became the faculty which required more policies and structures around hiring, firing, and oversight. And again, the limits of local control vary by state with some state legislators taking a fairly firm hand and others choosing to be more hands-off. The National Council of State School Boards Associations was founded in 1940 and school boards saw demographics shift towards schoolmen-lite; men - and sometimes women - from the community who wanted involvement in education without the messy work of actually working in schools. In the post-Word War II years, as the Baby Boomers showed up at school, school district boundaries were locked into place, often following lines that reflected redlining and other hallmarks of systematic racism. Functionally speaking, this meant that as some suburban school boards established their attendance boundaries, they purposefully put particular neighborhoods or housing developments outside or inside their lines. (However, and again this why "it's complicated" really applies here, some states during this era went with county-based school districts. This meant that school boundaries were set by county lines and school boards had no real say who went where.)

All of which is to say, in places where school boards wield a great deal of control, it's because, at one point, someone on the board identified the limits of their power and made the decision to push it as far as they could. Sometimes, state education leaders push back, sometimes they don't. Because "local control."