By not wanting his uncle to go to Heaven the audience learns a new side of Hamlet in which his thoughts are becoming increasingly rash and angry now that he is convinced that his uncle did in fact murder his father.
It demonstrates his instability and suicidal thoughts. While these soliloquies are, of course, spoken by the characters, they offer the reader some insight into Shakespeare's concerns about the human condition.
He wants revenge on his 'remorseless, treacherous, lecherous, kindless', uncle, but he can only complain to himself and accomplish nothing.
He wonders if he is a coward, since he does not 'cleave the general ear with horrid speech' or 'make mad the guilty and appal the free'. Hamlet walks in on his uncle who he believes to be kneeling in prayer, Hamlet at first thinks this will be the perfect opportunity to murder his uncle and gain his revenge but his soliloquy quickly reveal that his thoughts have brought him somewhere else.
This is more proof that Hamlet is depressed.
What makes you cringe?