Your astute question can be answered by considering the changing political environment of England, namely the changeover from feudalism to monarchy. Your question also must keep in mind that this particular part of Shakespeare's histories is a "part to the whole" and paves the way nicely for the amazing monarch, Henry V, the valiant leader of the troops against the French and a king worthy of all honor. Why? Henry V actually IS Prince "Hal" (sometimes called "Harry") in Henry IV, Part 1.
First, let's deal with the flux of England in regards to monarchy vs. feudalism. Feudalism, of course, was the system of lords and vassals and serfs that served as their own political entities during the middle ages. They were communities unto themselves with their own rules and leaders. At this time in history, England had moved away from this system and was concentrating more on honor paid to the one true king of England.
Let's look at the "disaster" of feudalism portrayed nicely through the aptly named Hotspur and family. They can be seen as the examples of this declining system. Hotspur is always described as a "rebel" and feels that only through this political rebellion can one restore the right order of the kingdom. Henry IV is almost swayed! In fact, there is a point when he considers Hotspur a better heir than Hal! However, Henry IV realizes the difference between a possible Hal in his youth vs. Hal in his future kingship and says in reference to the political rebellion of Hotspur:
Rebellion in this land shall lose his sway.
In this vein, it is also important to note that Falstaff, although influencing Hal at this point, is a simple, PHILOSOPHICAL rebel and NOT a political one. Hotspur is the true political rebel, and it takes Henry IV most of the play to discover this (even though Henry IV is never happy about Falstaff's influence on Prince Hal in regards to irresponsibility).
Now to delve into the subject of monarchy: England under one ruler instead of a bunch of feudal lords and vassals. Monarchy, one can guess, is represented nicely by the king, Henry IV, and his worry about Prince Hal, the heir to the throne. Henry IV is always talking about honor and, further, how important honor is to kingship.
In envy that my Lord Northumberland
Should be the father to so blest a son,--
A son who is the theme of honour's tongue;
Amongst a grove, the very straightest plant;
Who is sweet Fortune's minion and her pride:
Whilst I, by looking on the praise of him,
See riot and dishonour stain the brow
Of my young Harry
In this context he constantly worries about his Prince Hal and whether Hal can give up his wild ways and become an honorable king. Here, again, it is important to remember that Falstaff has lots of philosophical ideals that aren't really political. We can tell from the start that Prince Hal, although a wild youth, has an intention to fix his ways as he gets older. This is evidenced by the following quotation:
So please your Majesty, I would I could
Quit all offences with as clear excuse
As well as I am doubtless I can purge
Myself of many I am charged withal.
Another important hint of Hal's transformation from wildness to honor comes earlier in the play. Remember, when an Englishman talks about "the Sun" he is almost always talking about the king and the monarchy. Keeping that in mind, Hal says this:
Yet herein will I imitate the Sun,
Who doth permit the base contagious clouds
To smother-up his beauty from the world,
That, when he please again to be himself,
Being wanted, he may be more wonder'd at,
By breaking through the foul and ugly mists
Of vapours that did seem to strangle him.
Even though it is not within the confines of this particular play, put the previous quote in context of English political history. Henry IV recognizes that HE TOO was wild in his youth! This similarity acts to draw the two of them together and establish monarchy as a unit.
So as you can see, politically, Henry IV Part 1 is all about the honor of the monarchy of England that is nixing the anarchy found in the old, outdated feudalism of the Middle Ages. It is about philosophical rebellion (Falstaff/Hal) as opposed to true political rebellion (Hotspur). Honor is restored. Hal eventually becomes king and wows everyone with his dedication to the crown of England.