If school, not just business school and college, but even primary school, is intended to separate students destined to become high productivity workers from low, then good teachers, who help keep in school those students destined to become low productivity workers, and who help students destined to become low productivity workers pass tests intended to distinguish low productivity from high, these good teachers are interfering with the system, making it difficult for the rest of society to distinguish between low productivity people from high by looking at their education, a signaling mechanism in an imperfect (asymmetric) information game.
This model assumes that a person's productivity is exogenous: you don't actually learn anything in school, equivalently, nothing a teacher teaches ultimately affects productivity. Productivity might be entirely determined by the social support structure around a person.
Does this model explain teacher salaries? Society needs incompetent people, and only incompetent people, to be teachers. Promotion and firing have to be geared toward retaining and rewarding the incompetent. What mechanisms in the workplace and school system can accomplish this? Kind of a kakistocracy.
Education as a signaling mechanism has most famously been analyzed for labor and employment, but it probably gets used in other fields, too, like courtship. Good teachers might be indirectly affecting -- helping students subvert -- those fields, too. Flaws in the courtship process cause at best a waste of time, at worst, sexual and domestic violence between people incompatible with each other.