Is it possible that an increased demand for power is not satisfied by the amp instantly but after a delay during which the voltage drops?
Again... there is no increased demand for power. Amps do not 'push' power nor 'grab' drivers and certainly not demand more power than dictated by the voltage present.
As Otaku+ already mentioned the output of a music source provides a voltage. That is not a constant voltage but varies. That voltage has a limit. That limit depends on the design of the amp.
The maximum voltage also depends on the current capabilities of the same amplifier.
So when either the voltage reaches its limit OR the current reaches its limit (both have a limit) and it depends on what limit is reached first the output voltage clips. Yes, the output voltage can also clip because a current limit is reached and that can happen before the voltage limit is reached.
The lower the voltage limit and the lower the current limit and the lower the impedance of the headphone and the lower the voltage efficiency of the headphone the earlier the device 'clips' meaning the output
voltage clips meaning the SPL is limited.
When this happens and you turn up the volume beyond that point (depending on how 'hard' the clipping is) the loudness (volume) of the sound will still increase and bass levels will 'suffer' first as they have the largest voltage swing. The sound will turn 'nastier' but the volume of the sound keeps increasing but NOT the bass. That is clipped so stays 'behind'.
In these cases using an amplifier that has a higher voltage and or current limit moves the voltage clipping point upwards and so the clipping occurs at higher listening levels.
At some point, where peak SPL of 120dB is reached, the sound is so loud you won't go there simply because it is unpleasant for longer periods.
You can listen to 120dB SPL peaks for about a minute and this is impressively loud and because of equal loudness contours has tremendous bass power (makes Amirs earlobes shake). But you won't be doing that for long.
This means that when the amp chosen for driving your headphone can deliver the needed voltage (=
drawn power, not
delivered power) without clipping and the amplifier has enough gain and the music source has enough output voltage then having more available power is pointless.
Yes, having 3dB more headroom is desirable but not needed for normal listening levels.
When amplifiers (even a dongle has an amplifier inside) clips at SPL levels of say 90dB SPL in a specific headphone then it will sound as if it struggles with the bass. And it does. It clips the bass as that has the highest amplitude.
90dB SPL for bass is NOT loud at all. 90dB of bass is about 30dB above the hearing threshold.
60dB SPL of bass makes the fundamental of that bass inaudible already while the rest of the music is at a enjoyable soft background level.
90dB
A is loud and for bass fundamentals to reach that level the actual SPL = 120dB !!
So in short... when you want to use your headphone at all kinds of levels it needs to reach voltage levels that can make it produce 120 to 123dB SPL. You don't need as much if you never play loud. Around 110dB is good for comfortable loud and 100dB ensures normal listening levels never clip.
That said.. efficiency levels are often given at 1kHz or 500Hz. Looking at the frequency response of headphones you will find most of them roll-off and some 'boost' in the lows. This too has an effect of how bass is perceived. When you have to boost it the voltage limit is reached much, much, much earlier as well.
It is a complicated 'play' between headphones, voltage efficiency and voltage levels that can be reached which determine how impressive bass will be.
It is not costly to make amps that can provide enough to power all but very rare and inefficient headphones.
There you have it. It's all science not magic and the laws of that science cannot be broken.
Audio may seem like magic and things may seem 'inexplicable' but they aren't.
Aside from all these technical things that need to be right, including distortion and frequency response and in lesser sense phase, there are other aspect that also have great impact.
Seal of the headphone
Bass extension and frequency response
recording itself
dynamic range (loudness compression) also a recording thing
Hearing sensitivity (changes over the years, you don't notice this till it is really severe)
Taste (think bass heads)
The brain itself is also a major part of perception.
Nope... it is not simple and science is a part of it. Only that part is measured.