F=ma
P=mv
Pretty similar for these purposes. My point is that unless you punch with all of your mass at your top speed, then you are not using your full power. You are only using the power that you are fully capable of at that moment.
I may be nitpicking, and if so, I apologize. But if you have to slow down to hit harder, then you are not realizing the full potential of your body to generate power.
These are equations for point masses, which is a pretty poor approximation of the human body. The faster the fist moves and the heavier it is, sure; you can treat the fist as a point as long as it doesn't open on impact, I suppose. But the faster you throw a lightly packed snowball, the more mass it loses in flight. That doesn't happen with the body, but looking at that jointed assemblage as merely launching the fist as a projectile and analyzing it according to the equations of concerning point projectiles amounts to assuming the rest of the arm provides no drag.
Indeed, one expects, upon taking momentum to be your relevant quantity based on what you've written above, that
p(t)=m(t)v(t)
where
m(t) is the amount of mass actually in the projectile at the given time and
v(t) is its velocity, and hence some sort of line integral along the "flight path" will likely be necessary to draw any interesting conclusion.
I might wonder whether some notion of impulse is the right way to translate "power" here. In any event, I am not convinced that your equations make any sense. If I punch you, what's
m? The mass of my fist? Of my body? What's
v? The velocity of my fist? When? Instantaneously, at the moment of impact, or averaged over the punch time?