Well, the PoD for my current TL is too early for Yeonsangun to exist due to butterflies, but I'll provide some background for those who are interested. I skimmed the English and Korean Wikipedia articles, and although there were other factors, the main reason for his despotic reign was due to the conflict between the court and the monarch. This atmosphere was prevalent throughout Joseon's existence due to how the government had been structured.
Initially, after coming to power in 1494, Yeonsangun was a relatively able ruler, sponsoring the creation of several literary works and reestablishing a scholarly institution. However, in 1498, the first literati purge occurred because a scholar criticized Sejo, who established the line of succession at the time, as an usurper, causing the purge of the Sarim faction. On the other hand, in 1504, the second purge occurred due to personal reasons. His mother, who had been a concubine, had been sentenced to death by poisoning after she became jealous of the other concubines and began acting erratically, attacking the other concubines as well as Seongjong, the previous ruler. When Yeonsangun was finally presented with the evidence, he was shocked, as he had believed that he was the son of the previous queen consort. Soon after, he began to lose all trust in the court, and began to purge the officials indiscriminately, whether they were from the Hungu or Sarim factions.
His tyrannical actions included posthumously executing those who had been involved in his mother's death, along with killing those who remained silent, as they did not want to side with either the ruler or the opposition, and other officials for trivial reasons. He also killed two of the former concubines who had been involved in his mother's death, and caused his grandmother to pass away. Meanwhile, his actions became more erratic, as he began to construct a large pleasure ground by demolishing adjacent structures, costing a significant amount of the government's finances. When a short letter written in hangul was posted criticizing the ruler, he banned the use of the writing system altogether, even though its usage had not spread widely among the masses. Eventually, the officials grew tired of his dictatorship and staged a coup in 1506, replacing him with his half-brother. The new ruler, posthumously known as Jungjong, was also forced to purge some of his officials as rumors of the official closest to him attempting to usurp power began to circulate, showing how unstable the political environment was at the time.
In other words, although Yeonsangun only became mentally unstable during the last two years of his reign, his actions were somewhat blown out of proportion. However, his actions were much more brutal than other deposed or denigrated royals in comparison. Gwanghaegun, who was the only other ruler to not be assigned a posthumous title, was overthrown because he was illegitimate, even though he was an able ruler, and made steps to reform the military in order to confront the Manchus. Crown Prince Sado also behaved erratically, but it remains uncertain whether the officials fabricated the details in order to prevent a power struggle with him when he took power, or whether he was actually mentally unstable. Regardless of the reason, he was sealed in a rice chest, where he died from starvation. It was not until Heungseon Daewongun took power as regent that the ruling family managed to wrest power away from the court, although due to the quickly changing political environment overseas, it was too little, too late.
