Basic electronics? Basic electronics is that you need specific level of voltage to push driver forward/backward by specific measure. Which means voltage DIRECTLY affects volume. If you turn on high gain and turn the volume down to compensate, you output the same level of voltage in the end (and the same level of current and power as the result).

And no, "more voltage" doesn't improve driver control, the elimination of the voltage drop does. There is the only single measure you need to evaluate how the amp eliminates the voltage drops depending on the load, and that is - output impedance.