Public Education is propaganda
From the very beginning, one of its main purposes was indoctrination in the dominant ideology of the day. In nineteenth-century Europe, the goal was often to [indoctrinate the population in nationalism]. In the US, it was to indoctrinate European immigrants—many of whom were Catholic or Jewish—in what were seen as genuine American values, which at the time [incorporated much of the then-dominant versions of Protestantism].
Today, the goals of public-school indoctrination have shifted somewhat. But the fact of it persists.
This state of affairs throws cold water on the popular notion that we can use public education to solve [the problem of widespread political ignorance]. In principle, we might be able to increase voter knowledge of government and public policy by improving the school curriculum and requiring a high level of knowledge as a prerequisite to graduation. But, in practice, state education officials are usually more interested in inculcating students with their own preferred ideologies than in presenting facts objective or increasing political knowledge across the board. They especially aren’t interested in combating the [partisan and ideological bias] that infects many voters’ judgement of political issues, especially in [our highly polarized era]. To the contrary, they often seek to exacerbate that bias by promoting the agenda of Team Red or Team Blue (depending on who controls the state government in question).
Of course, school officials might take a different approach if voters closely monitored school curricula and refused to reelect politicians who use public school curricula for purposes of indoctrination. But if voters were that knowledgeable and that free of bias, we would not have a problem of political ignorance in the first place!