Rosencrantz

There’s a view that Rosencrantz and Guildenstern are interchangeable parts, and are further of minimal dramatic interest. They take care of some small connective tissue in the play, make Hamlet a little more relatable  Or maybe a little less annoying - with suck-ups like them, Hamlet is a comparatively down-to-earth guy. At one point, though, they have an unexpectedly important role to play. And that scene does a lot of heavy lifting.

It's the part where Rosencratz starts telling Claudius why Hamlet can’t be causing trouble for Denmark’s King, as it’s the whole nation that depends on his health. We find out about why they are there, why the two of them support Claudius over (the presumably senior in eligibility) Prince, and give one reason why Hamlet would not, in fact, find it easy to simply run the King through at some point. At the same time, they are giving Claudius a chance to show his guilty side, as they wax on and on about how far the King is above them and why regicide is a horrible, horrible act - to the point that even modern residents of democracies can themselves be doubtful of their ability to kill a king regardless of how deserved it is. 

And finally, they help to move the play along because, having given the King a chance to consider his guilt, they have maneuvered him to a state of mind where he gives himself over to prayer, dreaming of forgiveness and acknowledging his crime. And this is where Hamlet finds him, prepares to kill him, and instead reconsiders. Not for mercy, of course, but for much darker reasons. 

It’s also true, of course, that this is soon after the Mousetrap, and Claudius could feel guilty enough just from that. Rosencrantz twists the knife, though. Claudius might have taken his speech the other way, in fact, and acknowledged that he is the king, for all it was invalidly received, and that he can’t afford to feel guilt over the matter. If he gives up the crown, it goes to Mad Hamlet, and the country is much worse off than if he keeps it. 

A Reactive might have gone in that direction. If Claudius is a Hero, it would be like those other heroes (including, perhaps, his older brother) who have gone through the fire of war, and have little choice but to continue on, however broken they are from the effort. The Mousetrap reminds him of the sin, well enough; Rosencrantz shows him how more egregious it was than he had recently considered; the last thus instigates an impulse to pray rather than an opportunity for rationalization.