Why is Horatio HERE?

Hamlet, Act Four, Scene Five:

Polonius, dead. Gertrude, warned. We, the audience, have had Ghostly suspicions confirmed. Claudius has had his princely suspicions more than confirmed. And thus Hamlet, sent to England. Rosencrantz and Guildenstern, sent to deliver Hamlet (only never to return). Fortinbras, has marched his army through Denmark to kick the butts of the Poles. Ophelia, distract over the death of her father, and well on the path to suicide (though we haven’t seen it quite yet).

And as we wait to see it, Gertrude “will not speak with her” (IV.v.1). But she’s convinced to do so by a gentleman and Horatio.

Horatio?

Horatio.

Why is Horatio here, still in the palace at Elsinore, after his friend and his only link to the royal family has been removed and sent to England? Why isn’t he on his way back to Wittenberg?

And why is he giving advice as politically astute–and cynical (“’Twere good she were spoken with, for she may strew // Dangerous conjectures in ill-breeding minds” [IV.v.14-5])–as any Claudius ever presented?

It just doesn’t make sense to me…

Comment?