In Shakespeare's Hamlet, why is Hamlet less present in Act IV than he is in the previous three acts?

In Shakespeare's Hamlet, Hamlet is in
the first four scenes of Act Four to give Claudius reason to send him away (in terms of
the play's structure). Hamlet has killed Polonius, and Claudius realizes that it could
have been him. Hamlet plays his "insanity" game, leading the King's
men, especially Rosencrantz and Guildenstern, on a merry chase to find the body of the
King's dead advisor. It is not until scene three that Hamlet finally relents and advises
them where the body is. Now Claudius has good reason to send Hamlet away, and he tells
him that he is doing so for his own good.

It is in this
scene that we learn that Claudius has sent a letter with Rosencrantz and Guildenstern
(who travel with Hamlet) to deliver to England's king, asking that Hamlet be executed
(as a favor to Claudius). Scene four shows a chance meeting with Fortinbras' army and
Hamlet, giving Hamlet another reminder that he
must act, with honor, to avenge his father's
death.

I believe that it is Hamlet's absence that allows
Ophelia to lose her sanity. If he had seen her worsening condition, he might have been
able to help. If nothing else, he could have kept an eye on her to make sure she was
kept safe. With Hamlet out of the picture, and Polonius dead (though he doesn't seem a
particularly caring father who forever sends his daughter out to spy for him and the
King), only the Queen can act as an advocate, and even that is not enough. Of course, in
terms of the play's structure, once Polonius, and then Ophelia die, Laertes—with some
help from Claudius—believes Hamlet is to blame. The final scene that abounds with
villainy and tragedy is set in motion with the death of the King's advisor and his
daughter. Shakespeare clears the way for all of the remaining characters in the play to
be killed by the King's treachery.