Prince Hal as "Mankind"
Structurally, Prince Hal is at the centre of the play, pulled in at least three different directions: towards Falstaff and the pleasures of the the tavern; towards Hotspur and an ambitious pursuit of honour; and towards his father and a Machiavellian use of power*.
Perhaps Hal is like Mankind in the morality plays, tempted by those around him to neglect the right rule of order. Certainly Falstaff, at one stage is explicitly likened to the Vice of the moralities.
Though Shakespeare does not explore it in detail in the play, there was a reasonable doubt as to Hal's legitimacy as heir: Hotspur is not necessarily wrong when he chooses to espouse the claim of Mortimer.
Footnotes
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The dark side?
See, for example, the advice that Henry IV gives Hal in the scene of their confrontation, 3.2.39ff., and the use Henry makes of others in his clothes at the battle of Shrewsbury (5.3.25-28).