As I see it, their real incentive would be to shut down the higher education system, because it a) costs money, b) sends a good part of produced talent to other countries, and c) produces educated citizens which are harder to manipulate.
Sadly, I hear quite a few confirmations of this from friends who work in education.
BTW, here's a great video, Rules for Rulers, which is basically a video TL;DR of "The Dictator's Handbook" that explains incentives of democratic and autocratic rulers: