Another thought struck me recently regarding Shakespeare's use of poetry (and I'm not referring to the verse only; even his prose is poetic). As we listen, we are very much aware that people don't speak in those ways - this was one of Tolstoy's beefs about Shakespeare, in fact - but we're also aware that people do feel in those ways. And like with music or dance, we know that we're witnessing an exaggeration, but what this exaggeration leads to is of such depth that it's unlikely that it could have been found otherwise. The poetry, therefore, helps us to think certainly, but just as importantly, it allows us to empathize emotionally.

Also, the poetic language makes us immediately aware that we're watching fiction (even when historical sources have been consulted), but the quick establishment of this fact permits the mind to go past the surface issues of story-telling and veracity to get to the real psychological and philosophical content. For an example, here's Cassius speaking to Casca (1.3) about the reasons for Caesar's ascension; in his opinion, it's merely a symptom of Rome's weakness. Note the poetic content of the words and the emotions they release. Then imagine the danger in even thinking them:

And why should Caesar be a tyrant then?

Poor man! I know he would not be a wolf,

But that he sees the Romans are but sheep:

He were no lion, were not Romans hinds.

Those that with haste will make a mighty fire

Begin it with weak straws: what trash is Rome,

What rubbish and what offal, when it serves

For the base matter to illuminate

So vile a thing as Caesar! But, O grief,

Where hast thou led me? I perhaps speak this

Before a willing bondman; then I know

My answer must be made. But I am arm'd,

And dangers are to me indifferent.