In Hamlet's soliloquy at the end of Act II, scene 2, why does Shakespeare show us Hamlet thinking up his plan, rather than just revealing it?

Hamlet has been wrestling with his conscience for several weeks since his father's ghost spoke to him and asked him to get revenge against Claudius.  We know that about this much time has passed because Laertes has had enough time to get to Paris, to have run out of money, and to have written home asking for more.  When the ghost of King Hamlet appeared to his son, Hamlet believed what the ghost told him, but since then, Hamlet has begun to doubt the ghost's honesty.  He doesn't know if the ghost he has seen is a devil luring him to hell by getting him to commit murder or if he is truly his father's spirit (see the last 8 lines of this soliloquy).  He decides that the play will reveal Claudius's guilt, if there is any.  Shakespeare shows us Hamlet's thinking here so that we understand why Hamlet rewrote the play for the performers.  When Claudius reacts as he does in Act 3 to the rewritten scene depicting how he killed King Hamlet, we understand why he has that reaction.  We also better understand Hamlet's odd behavior before the play and immediately after the play.