Do they? They tend to have the highest hp, no?
As well, it's only an issue if the hp cost is too high; the math would have to be done to make sure it's reasonable. I am sure that's possible, though. It would also put the decision in the hands of the player: it might be fun to burn some hp to go for this big maneuver, or I could play it safe and do a vanilla attack.
Finally, it would address the issue of the adventurer who is just as effective at 1 hp as they are at full. Under this system, "No, you're not" because you no longer have the energy to pull off the maneuvers that make you a badass.
So I finally got to page 6 or so, and saw that
@Fanaelialae mentioned something similar regarding adrenaline. It's basically what I am saying except we would be using a pre-existing resource.