Sorry, I'm having some trouble parsing that, and that's partly or mostly on me. The world of audio (audiophiles, recording / studio types, etc.) uses words in different ways than I am used to seeing. Let me know if I'm getting something wrong. It's mostly that I'm not clear on what precisely you mean by "greater dynamic headroom" and "peak dynamics".
If you turn up or down the volume, you're not changing the dynamics, the difference between the louder and softer sounds. You're just scaling everything. You get the same peak dynamics and everything else. There are arguably two exceptions, the way I see it: (1) you crank the volume so far the amp can't handle it so it clips the loudest part (won't happen unless the max power output capable is too low), and (2) if the softest parts are quiet enough and the room ambient noise is loud enough and the overall volume is set low enough, then the soft parts are drowned out by ambient noise and effectively lost unless you turn up the volume.
At any given point in time, the power being drawn by the headphones depends on the signal level. It's changing constantly; it's more for the louder parts and less for the quieter parts.
An amp capable of higher power output allows you more headroom in the sense that you can turn the volume up higher before it clips. Is that what you mean by dynamic headroom?
Also, for clarity, please be careful in distinguishing between output levels (that you're hypothetically running) and maximum possible output levels a device is capable of. The output level is whatever you set. The max level is a physical limitation of the electronics.
Edited by mikeaj - 5/1/13 at 9:31am