It is, and article hit pieces like this are exactly why it will continue to expand. Newsflash, there’s an actual large portion of the population that more and more doesn’t want what is taught to their children regulated by the government.
Obviously I'm presenting an extreme example, but society at large has a vested interest in ensuring that children, broadly, are educated. I'm not saying there are no problems with regulations, but I hate how the "deregulate everything!" crowd conveniently ignores the reasons those regulations were created in the first place.
And society should also care whether government-run public schools are doing this--not to mention whether they are indoctrinating children with values that many parents disagree with.
School boards are elected, but I don't think "broad democractic oversight" is a fair description.
In any case, none of the things you mention prevented the US public school system from being explicitly set up to indoctrinate children, as explicitly described by the people who set it up. So to the extent that society in the US cares about educating children, it cares about educating them according to a particular political agenda that many people do not agree with. That is a major reason why homeschooling continues to increase in popularity.
Not all homeschoolers are like this. There are plenty of other good reasons for parents not to want their kids to go to public schools.
> society at large has a vested interest in ensuring that children, broadly, are educated
Yes, but for whose definition of "educated"? In the US, at least, the government was not supposed to decide that. Individual families and communities were. And, as I have posted elsewhere in this thread, the people who set up the US system of widespread, compulsory public education were quite explicit about what they meant by "educated", and that included plenty of things that any reasonable person would consider to be indoctrination, not education--and that was on purpose.
Saying that the cost of giving persecuted minorities an out is "then we might not be able to persecute the minorities that I've decided actually deserve it" just feels fundamentally unconvincing.