I think the problem is entirely structural. The categories are wrong, they are construed as “levels”, ie, ranks, therefore they are interpreted directly as a social ordering, which causes parents to push for their kids not be classes in “lower” levels. Why not just have education open for everyone and have in the same curriculum options for both Latin and Blacksmithing?

“Hunt in the morning, fish in the afternoon, rear cattle in the evening, and criticize after dinner” and “every cook must learn how to govern the state”.