The innerfidelity (Musings...) article mentioned above purports to be looking at a high (for audio) frequency electrical resonance. The author has modeled it using an equivalent electrical series LCR circuit by assuming that the mechanical factors can be fully represented by 3 lumped series resistive or reactive elements. The ringing he shows as a result of electrical under-damping of this resonance is at about 6KHz. Very many headphones do indeed have a pronounced acoustic frequency response peak at around this frequency. If the transducer mechanical behaviour (to include air resistance, surround/suspension compliance, membrane breakup and anything else relevant) is fully modeled by this LCR electrical network, then it is possible, for some headphone resonant equivalent LCR values, that a high amplifier output impedance could improve this particular situation and bring it closer to a technically optimum critical damping situation. If this was achieved, the acoustic peak would be greatly diminished. In practice, I don't think all the electrical and mechanical factors are fully represented by the electrical model at this sort of frequency.
Usually we are talking about low frequency primary resonance, which is more typically at around 100Hz. Headphones usually have reasonable mechanical damping here. This LF resonance has been typically modeled by others as a parallel LCR circuit. A pure parallel LCR circuit will be damped very quickly with a low output impedance.
It seems to me that it follows from all this that it depends on what the electrical model of the electrical/mechanical resonance you are concerned about looks like. Most headphones have several peaks/resonances. Certain resonances may be close equivalents to a series LCR circuit, perhaps the HF ones. If so, those particular resonances may be better damped and therefore less obtrusive with a higher amplifier Z out. The primary LF resonance of a headphone, if, as seems likely, best modeled by a parallel LCR circuit, will very likely be optimally damped by a low amplifier Z out.
if the innerfidelity article author is correct, I would think that higher amplifier Z out might produce better HF damping for some peaks. It would likely give worse LF damping. Steady state sine wave testing with various z out values does not seem to change HF response much. My conclusion would be that the mechanical resonances in headphones cannot be accurately mapped into simple electrical parameters presented to the amplifier. They cannot be corrected much by choosing output impedance. That is not to say that output impedance might not affect them somewhat, especially in the dynamic music signal situation.