No Vote, No Voice

Maybe someone can explain this to me: why don't we elect the school board? I've heard some locals say that ordinary voters can't be trusted with such an important task.
That's silly. With that rationale, no one could vote for anything.
When I was a reporter, I covered a school board for many years. The superintendent went through an arduous process -- her salary was publicized before it was ever voted on. She went through a yearly review. School board members, who were voted in by their neighborhoods, with 2 at-large members, were accountable for their votes.
Recently I've heard some argue that an elected school board gives the "squeaky wheels" too much say in how schools are run or where they're located. It's usually these citizens who are speaking on behalf of their neighbors, who should, indeed, have a say about something as important as new county schools.
I'm not talking about dictating specific curriculuum. But here's an example of something that wouldn't have happened if the public had a voice: the block schedule. This was implemented with no data and no way to collect data to rate its effectiveness. And whether it's true or not, the community perception is that the school board demoted one of the few who was keeping track of the effect the block schedule had on test scores and student progress.
I contacted the school board during the last redistricting process and received the equivalent of a pat on the head and "don't worry. It's not really all that bad." What incentive did this member have to offer me any more? I'm not saying that all school board members are self-serving, I'm just saying, shouldn't we be the ones telling them just how long they're going to serve?