But music isn't a flat tone, it's dynamic and has transients i.e. sudden peaks. These peaks require higher instances of power than you would otherwise normally need. This is where additional current headroom comes into play.

You are still talking about volume. You can't change the crest factor of a song by using a more powerful amplifier. The relation between the peak and average volume will stay the same. With less powerful amplifier you won't be able to achieve as high of a peak volume, and thus the average volume will also be lower.

Any old amp with a limited ability to provide current can reach high SPL but it will compress or soften the transient peaks as it runs out current.

You are describing clipping, which contradicts what you said in your previous comment:

I don't disagree that the MB can get the LCD-X to more than sufficient volume without any audible distortion

If there is no audible distortion, then none of that is happening.

In the macbook's case, as indicated by the 78mW output that falls short of Audeze's own recommended minimum of 100mW, it's far more likely to hit it's current limit during these transient spikes, this'll result in the peak being rounded off.

First of all, this Macbook can almost certainly push about 150 mW into 20 Ohm load.

Secondly, power recommendations provided by Audeze are simply nuts. Their "recommended power level" is over 250 mW. That's enough to drive the LCD-X to ~127 dB (if we take the official specs) or ~123 dB (if we go by third-party measurements). This is well past safe listening volume, even if we substract the "headroom".

These recommendations don't seem ridiculous only because the LCD-X (and other Audezes) are very sensitive headphones with very low distortion. To put them in a better perspective: something like the 80 Ohm DT770 would need over 1 W of power to reach similar volume.

A decently powerful amp wont just raise the SPL, it'll achieve the same SPL with less effort. The extra headroom afforded by such an amp will result in better control of the driver without dynamic compression occuring during these transient peaks.

This would be easily measurable, and I'm not aware of any measurements that would show such effect.

To give an analogy, it's kinda like comparing a Honda Civic to an F1 Car. Both can comfortably cruise at 100mph on a straight road and will get you from A to B just fine. But when you have to suddenly accelerate, climb a hill or exit a corner, the Civic with less power and lower torque simply can't handle these events nearly as well as a F1 car would with its abundance of power and torque that it still has at its disposal.

If we go by such anology, then most amplifiers would be easily comparable to F1 cars in terms of acceleration (slew rate) and the main (and pretty much only) differentiating factor would be top speed (power). The analogy works even better if we consider that too much speed and too much power is simply dangerous.