The Bad Sleep Well is not a Hamlet
Hamlet is not just "a guy gets revenge on his father's killer". That's not even the main thing! The emotional core of Hamlet is the drama between the prince and the other members of the court: these people he's known as his life, his own mother, are all backing Claudius, and only Hamlet (and Horatio at Hamlet's urging) believes him to be a murderer. It's the tension between those two understandings of the world, and in Hamlet's doubts of his own purpose, which are the core of it. If the Claudius equivalent isn't at least metaphorically marrying the protagonist's mother as well as ascending to the throne, it's not a Hamlet.
(The Lion King isn't a Hamlet either for the same reason. Scar does literally marry Simba's mother, but absolutely no one is chill with it.)
having just watched a Hamlet for the first time in years, I was absolutely right about this. Hamlet's struggles with isolation, with his mother and Ros and Guil and by the end even Laertes buying into this false vision of a world where Claudius is a deserving ruler, is the emotional core of this play and the specific dynamics of vengeance for the murder of the father is just structure to bring that to life.
His madness is inversely proportional to his confidence that he's right—once Claudius reacts to the play-within-a-play he's finally able to break out of his indecision and talk to his mother, and once he sees Claudius's letter asking England to execute him he comes fully to himself. Which means in turn that the madness isn't just grief or rage, it's specifically the dissonance between his implacable sense of injustice and the world around him screaming at him that everyone else thinks everything is normal. A particular poignant mood for the present day.
