Hamlet as the outsider really give the readers and watchers (if being performed) a critical connection to Hamlet that would not otherwise have been achieved. We get drawn into Hamlet's revenge plot and we find ourselves urging him on toward a bloody revenge. We truly feel his emotions because of the use of soliloquy throughout the play. We are angered when he is angered and we are disappointed in him when he is disappointed in himself. I don't think the play would have been nearly as successful without these connections made through Hamlet's isolation. It's a special treat for the readers and watchers when the narrative is interrupted to get us inside the mind of Hamlet. We acquire an understanding of his desires that we would not otherwise be able to attain.
That is such a good question - I feel like I'm doing brain-aerobics trying to figure it out! :)
I think Hamlet as an outsider results in the audience being sucked into his mind and his emotional/mental state through the use of soliloquies. This poor guy has no one to turn to except Horatio, who is probably trying to be a bit too over-protective of Hamlet (which chafes at him a bit). So who does he share his thoughts with? The readers/audience. If he weren't such a loner, going through the pain and confusion he's going through, he would have someone else he could turn to. But as it stands, there's really no one he can trust, which turns him inward to his own thoughts.
Shakespeare's brilliant use of the soliloquy in this play not only lets us into Hamlet's tortured thoughts, but it's like having a pause button on the play - it's like things are going along at Elsinore, la dee da, then suddenly someone hits PAUSE and we get a close-up looksy into Hamlet's mind. So the narrative itself comes to a screeching halt while we learn more about what's happening in his brain.
Thanks for the great question - I hope I did it justice with my rambling thoughts! :)