That's an incentive alignment problem. It is the responsibility of management (state and district admin) to ensure that what is best for the teacher's career is also what is best for student education.
I'm not too familiar with the details of management here, but is it even possible for public schools (and other government operations) to have proper incentives given voters don't care about results? I suppose "school-choice", which happens to be vehemently opposed by Democrats, would be the only way.
Not sure what you mean by “optimizing local maximums at the expense of everything else”. It almost sounds like an argument but there’s no substance.
You claim that public education should focus on the lowest common denominator so we can avoid an underclass susceptible to manipulation. That’s both a weak justification to purposely damage public education and condescension shown by elites when poor people don’t vote the way “they should”.