I think majkel actually already did a good job of it...but lets see...I'm hoping in simplifying I'm not distorting any of the original detail but the "oversimplified version"
Big power supplies with appropriate capacitance for the required load are much more common in speaker amps than headphone amps,
the ability to operate driving a sustained high current draw while still having sufficient reserves for peak swings is also much more common in speaker amps than headphone amps. Any amp can drive xx current, with xx current peaks, and even drive xx current sustained, but being able to drive high current sustained while not running thin on reserve power to swing more (as majkel said, especially in terms of voltage swing) for peaks is a larger challenge in terms of the power supply and heat dissipation. The wider the dynamic range of the music being played the greater the sudden swings to peak from the nominal output, the greater the need for reserve voltage.
On the flip side, the qualifier here would be "within a certain limit." The need for 200W monoblocks totaling 400W power is still probably better used with a 16" subwoofer or some Maggies
HE-6 needs a lot of power, but it doesn't need more power than the average pair of floor standers with dual 8" woofers.
Though with my latest toy I'm broaching closer to that at 140wpc....but that's way more than needed. The big transformer to sip from helps though.