The difference between the Church’s education and state education is that the Church’s future was dependent upon the production of capable peasants – and so the priests, brothers, and sisters were economically ACCOUNTABLE for at least the social and economic results of their efforts. As the product of what remained of catholic education myself, the near military discipline, was almost as good as the military discipline of the military schools (Which I begged for and couldn’t get).
The problem with contemporary education isn’t just that the schools aren’t run by the nobility, they aren’t staffed by talent, but the bottom end of the education system, and the staff and the administration are not dependent upon, and accountable for, their efforts.
The problem is worse in the academy, where, like the sale of medieval indulgences, the new academic religion is incentivized to maximize the throughput of students, in exchange for a diploma that grants them access to the workforce.