Why does Arthur Miller mention Judges Stoughton and Sewall, but not present them dramatically within The Crucible?
I assume he just did it because he wanted to do it that way. Once you already have Danforth and Hathorne as judges, what do you need the others for? I imagine he could have chosen to have Stoughton and Sewall rather than Danforth and Hathorne. But once you have two judges as major characters, it seems like two more would not really do anything for your play.
So I do not think there is any really big reason for it. I think it is just that you can only have so many people as major characters in your play and he didn't have room for them (any more than he had room for any of the victims who never show up).