Why does Miller end the Crucible when he does?

After the dramatic events of Act IV, Miller closes the play with Proctor choosing to be put to death in order to preserve his good name. The Puritan judges have forced Proctor into an impossible and paradoxical situation: If he lies and "confesses" to being a witch, his life will be spared. If he denies that he is a witch, he will be put to death for "lying" and refusing to "confess," since the accusations alone have already "proven" his guilt. At first, Proctor plays along with them and "confesses," but once the judges ask him to sign his name for the whole community to see, he refuses. He delivers his most famous lines here, explaining why he refuses to sign his name to the confession:

"Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul; leave me my name!"

The abundance of exclamation marks indicates his outraged, passionate state of mind. Here, he realizes that the rest of his spared life will be a fraud, since he has earned his freedom through lying rather than refusing to play by the impossible rules of the court and keeping his morality intact. While this passage is one of the most powerful moments in the play, the actual ending of the play gives Elizabeth, Proctor's wife, the last word. She says, "He have his goodness now. God forbid I take it from him!" Her statement reaffirms Proctor's redemption. Although he is a deeply flawed man who has sinned and feels tremendous remorse for his actions, he still finds a way to serve his community and take a stand against the insanity that has swept through the village. Ultimately, he dies a martyr, giving his life to preserve his name and to fight against the unjust hysteria that has corrupted the community. With that, the audience might feel a sense of peace, as they know that history will vindicate the innocent victims of this mass hysteria. Proctor, then, can die a hero.