Political strength is just one kind of power in Henry VI, Part 1. There's also military power, rhetorical power, supernatural power—and if you're a king, you're sort of expected to have them all.
You're supposed to be a good ruler, using your political power well; you're supposed to be kick butt on the battlefield and inspire your troops with your military power; you're supposed to give great speeches and amaze your troops with your rhetorical power; and while you don't need to be a saint, you are expected to be good enough to get God on your side as well. Not to mention the Pope, who's got major political power in this era. No pressure or anything, though…
Trouble is, other people seem to have a lot more of most of these kinds of power than King Henry VI does. Talbot and Joan are way more impressive on the battlefield, for instance, and Joan appears to have supernatural powers galore while Henry doesn't possess any at all. At least Henry may turn out to be a decent public speaker. But given the choice between a king who did well in Broadsword Fighting 250 and a king who did well in Public Speaking 101, which do you think the nobles prefer?
Questions About Power
Is there a single most powerful character in this play? Or is power split up among different characters?
What kinds of power would Henry VI need to grow in to be an effective king? Does he show signs of doing that?
How much power do the French have? What kinds of power are they most successful at leveraging?
Are there any kinds of power one doesn't need to get on in the world of this play?
Chew on This
Though she's ultimately captured, Joan is the most powerful person in the play because she claims power for herself against the most odds.
Henry's lack of several forms of power doesn't matter—as king, his status makes him more powerful than anyone else.