In China, since the establishment of the imperial examination system, most scholars have studied for the purpose of being an official, and few people have studied for the purpose of being an official.
Once a scholar aims to be an official, there will be some problems in the relationship between teachers and students, so I won't talk about it here. Just talking about the disadvantages, in the Ming and Qing dynasties, the relationship between teachers and students who were officials in the same dynasty was often the closest political force. Many people are willing to be examiners, because whoever is an examiner, this year's candidates are nominally your students. Which is the basis of your future regime.
Once this happens, there will be all kinds of political gangs. This has always been the biggest problem in China officialdom. This is the root of political corruption and political chaos.
This pernicious influence has always existed, and many leaders have gone to archives schools, not for further study, but to cultivate relationships. Once a relationship is established, it paves the way for your promotion and wealth.