So why is he remembered as an incompetent, retarded dickback? He prosecuted Christians in his reign

I don’t think that the persecution of Christians factors into this - many other emperors did it that we remember fondly.

I just think that he wasn’t very good at the propaganda game. Many historians belonged to the senatorial class, which was at odds with the emperor (all of them), and Nero was not able to counter that.

Impartiality - or a lack thereof - is a problem that we face with a lot of historical figures. I very much doubt that Xerxes flogged the Hellespont, for example, but the Greek historians loved that tidbit because it showed his hybris. Same with Nero playing music while Rome burns.

From what I remember of my studies, he was a “good enough” emperor, especially in his earlier years, but didn’t know how to play the political game at all. The senate hated him (but honestly, they were a corrupt bunch who hated pretty much everyone), and a lot of people around him attempted to use him for their own political games, which eventually made him grow suspicious of everyone else.