As a general rule this is true. However in my experience there is a segment of this market in the US that is extremely lucrative; essentially the top X% of public high schools. These schools are private for all intents and purposes, as most of their budget comes from property taxes. These schools have massive budgets that approach $100 million, extraordinarily qualified and perceptive teachers, and a community that is heavily vested (and almost neurotic) in the success of the students. Also, the staff at these schools are surprisingly tech savvy, often with a large dedicated budget for technology.
All the above factors combine to create a perfect storm for a business with an innovative product. If you've got a product that will make students at these schools more competitive in the college admissions process, it will be purchased at a massive price tag. All the key players, the parents, the teachers, and the administrators, have the will and the budget to make these types of acquisitions.
Note, marketing to these schools is difficult. A connection in the administration or the education space is the easiest way, but I'm convinced you could bootstrap yourself through the teachers. They are smart and savvy and the senior teachers can have surprising influence. Further, the market is on your side. One you convert a few of the top schools in the area, it is likely most of the other top schools will follow, as not to be left behind. Top schools will follow the leader, as these things go.
Overlook this market segment at your own peril. :) There's only a (relatively) small set of schools that fit the above criteria, but they have a combined budget of billions nation wide.
You may note that I did not mention the top %X of private schools. That is because in my experience, parents (one of the key players) aren't necessarily as invested in the school on a day to day basis. There seems to be a higher rate of apathy with parents in top private schools, whether as a result of geographic separation or some other factor. The bottom line is that at top public schools, the parents made the effort to move to the community, buy a house at a ridiculous value, pay outrageous property taxes. In practice that seems to create a much more invested base of parents that will be much more involved in the school. I still think you can sell to top %X private schools, but it seems harder in my mind.
If someone is thinking about starting a product in this space, happy to chat via email.