18V power supply and diode clipping

[Ngr]

Am I wrong?
I assume that in an IC based distortion-overdrive device, an 18V power supply will allow an higher voltage swing at the output resulting in a greater dynamic range and less compressed feel.
But what's the point in doing that if usual configurations of clipping diodes (or any clipping device being used) will indeed clip and limit the voltage swing between 0.3V and 1.7V depending on the configuration no matter what's the power supply voltage is?

[guitar.mod]

Am I wrong?
I assume that in an IC based distortion-overdrive device, an 18V power supply will allow an higher voltage swing at the output resulting in a greater dynamic range and less compressed feel.
But what's the point in doing that if usual configurations of clipping diodes (or any clipping device being used) will indeed clip and limit the voltage swing between 0.3V and 1.7V depending on the configuration no matter what's the power supply voltage is?

If the clipping devices (diodes) are connected at IC negative feedback path (typical configuration for overdrive) - then there is no benefit from higher supply voltage except some possible technical benefits/drawbacks not related with "greater dynamic range" feel, like noise, current from power supply, slew rate and etc.

If the clipping devices (diodes) are connected at the opamps (IC) output (without any other signal limiters) - then there will be less "harsh" opamp saturation, - and then, at high gain settings, you will hear less harmonics that are generated by opamp (IC) saturation (and then it brings back from saturation) when power supply have more voltage (18V). In this case, At the output signal appear harmonics generated by clipping diodes and by opamp itself. Maybe there will be "more dynamic feel". If you will be using only low-mid gain settings - the effect of higher voltage could not be noticed.