I agree with #2 that Hamlet's rantings bring him near madness, but isn't this the whole point? I see madness as a prominent theme of the play, it is one of the driving currents that make it the tragedy that it is. Without the madness, without Hamlet being so emotional over the situation, the play would never erupt and end in the deaths of everyone at the palace and it really is quite a dramatic ending. As a play being performed I think that Hamlet's rantings are essential, they give the audience the insight they need. It is inside these soliloquies that the audience connects and becomes empathetic toward Hamlet. It is the first soliloquy that really draws the audience in because we can identify with how infuriating it must be for him that as a young prince he has not only lost his father, but he's lost him to his uncle's hand who married his mother while his father's corpse was still warm in the ground.
Hamlet's situation is obviously a difficult one, but in his first soliloquy (as well as the rest of the play) he is intensely dramatic about it. He harps on his own situation by contemplating suicide and wishing death upon himself. He enlarges the wrongs against his father by dwelling on the past between his mother and father and by repeating the period of time (less than two months) that has passed between the funeral and the remarriage. He also makes several comparisons (his mother to a beast, his father to his uncle, himself to Hercules, his mother to Niobe, etc) to stress the horror of the situation. This type of ranting could only be useful as an initial release of emotions, giving Hamlet some time to expel his emotions, but dwelling on these thoughts is what brings him to the brink of madness.