In "Hamlet," why does Hamlet insist that Horatio remain alive? What must Horatio do for Denmark?

In the last act and the last scene, Hamlet insists that Horatio remain alive to tell his story. To make sure that everyone knows Claudius was the one who murdeered his father and that he, Hamlet, was not responsible for the deaths of  his mother.  Horatio, was to make sure that everyone knew that Fortinbras was to get his vote for King.

“O good Horatio, what a wounded name that is,
“O, I’m dying, Horatio,
The potent poison quite conquers my soul.
I cannot live to hear the news from England,
But I do predict that the throne belongs
To Fortinbras. He has my dying vote,
Tell him so, with the news, more and less,
Which has been asked for. The rest is silence.”