Question

Why do you think Miller uses this unusual expository strategy for his drama?

Answer 1

The thing to note about The Crucible is that it is a play.  As such, narrative is something that plays are certainly not known for.  The main elements of a play are the lines (dialog) of the characters and typically stage directions.  That said, there is, in fact, a lot of expository writing within the The Crucible.  This is so because there are a lot of intricacies that would otherwise be difficult to communicate to readers via character lines and stage directions.