Heres another attempt to try to explain why i think i get better drive on my headphones using low ESR caps.
Imagine an amplifier with a load connected (speaker/headphones) supplied with an audio signal.
This amplifier will, aside a pre bias, draw current from its power supply. but this current is not fixed when playing music.. it varies with the signal it amplifies.
The more force is needed for a conus from a speaker driver to be pushed or pulled, the more current the amp draws. of course for headphones this is only in mA range.
In fact the amp's current drawing behaviour can be observed as audiosignal related current modulation on its power feed.
If it would be a fixed current, the PSU would just supply it, but the voltage on the amp would be slightly lower cause the dropped voltage will exist over the circuit's wiring and tracks. As long the PSU has enough rated current specified this voltage drop would not matter much.
But with a varying current, as a result, also the voltage will vary, and this is applied to the amp which in turn wil vary its amplified output together with it.
So while the audiosignal demands more force on the speaker driver coil, the voltage on the amp is slightly lowered, counteracting the output causing a form of distortion.
Distortion which is not so much obvious with a clean sinewave test signal and would not appear that much on measuring.
Now PSU's are equipped with capacitors parallel on the output for ripple rejection, not to be mistaken with RF filtering caps.
These capacitors serve another important purpose in acting as a voltage buffer. When a rising current (peak) is drawn, the capacitor will help supply it with its contained energy keeping the voltage steady.
An audio related current ripple (in a frequency range of ~20-20Khz) is too fast even for a small capacitor container to react to (unload and load again)
But a resistor does not hold energy charge and will instantly allow a voltage drop causing the above discribed effect. Resistance is everywhere on a circuit board, like plug contacts, components, wires and PCB tracks, all sum up to total resistance before the dropped (and modulated) voltage reaches the amp.
Capacitors have a notably internal resistance in series with their energy container called ESR (Equivalent Series Resistance) which can be several hundreds of miliohms.
This might not sound as much but it allows a ripple to be built up on the voltage.
Many (audiophile) external PSU's are loaded with parallel capacitors mainly to increase the capacitance and lower the AC-DC ripple or PWM ripple in case of a SMPS.
And posess a lower ESR than a 'standard' PSU like in Dave.. this will not so much lower RF.. but give benefits in the drive capabillity of the amp section. I can imagine why i heard and users say these PSU's matter.
But as stable voltage an external PSU might give.. the voltage still suffer a modulated drop while running through connector contacts and pcb tracks.
As most amps, Dave has capacitors placed close to its amp section for mainly the same reason: stabilising the voltage feed on that circuit.
But i think this can be improved by lowering the caps ESR values to decrease the current modulated voltage and with it the amp's performance.
Principle: smaller ESR makes less modulation amplitude
Aside the amp, also Dave's LM307/317 regulators react to varying input voltage, they are based on a feedback to keep their output at the set voltage.
If the input voltage drops, they raise the output current to level the voltage, this gives a delay on the audio related ripple which in turn also influence the performance of the amp. Placing additional caps on the input of them contributed also on stabillity.
Thanks for reading.. i hope this makes any sense
Cheers