Absolutely agree as a technical matter that being able to swing full voltage at 20 kHz is better than not being able to. The SRX Plus, for example, is not able to do so, and in fact, as I posted in that thread, actually measurably rolls off at lower frequencies as the output voltage increases (it's flat at 100 VRMS to over 20 kHz which is pretty loud, though). BTW, KG's calculation is actually a minimum estimate of the current required, because a stat headphone is not a capacitor - it makes NOISE, e.g. music, which means it has to consume ADDITIONAL current over what a capacitor requires.
However, as Dr. Gilmore points out, the question is, how loudly do you listen and how much actual audio content is there at 20 kHz. There is actually some data on the latter point. A number of years ago, Peter Baxandall and Nelson Pass both measured slew rates in recorded music and both came to similar conclusions, namely that an amplifier capable of reproducing a 6 kHz sine wave (yes, 6 kHz, that is not a misprint) with low distortion is adequate for music signal, because of the natural roll-off of musical instruments. Note that this was equivalent to the fastest music signal they found, and that everything else they measured was SLOWER than that. More recently, Baxandall published that he had found a recorded music signal that required an amp to be capable of reproducing a 15 kHz sine wave with low distortion. That is significantly faster, and in fact is within striking distance of the 20 kHz signal at full output voltage requirement - however, it must be noted that this is a unique event, and for almost all music the lower requirement is adequate. Is it appropriate for a state of the art amplifier to aim for the more stringent requirement? Absolutely! Will the lower requirement suit the needs of most? Probably. Of course, extra headroom is always nice - but there is a cost. For Stereophile Class A, the cost is always worth it, almost by definition. For Stereophile Class B, the question is, how much can you cut back for as little sonic cost as possible.
Finally, if you listen at lower levels, the requirements decrease accordingly. This is why spritzer suggested to Tyll that he listen to electrostatic headphone amps at high levels to differentiate between them - because this stresses the amp the most.