Those of us with a little technical knowledge accept and expect it because at lower frequencies dynamic loudspeaker driver output is proportional to voltage.
The statement is ambiguous. We know that doubling power is 3db, and that there is or should be a direct correlation with driver output. Since this is so then driver output is also proportional to power.
Quantity becomes quality when it avoids clipping
This is a bit of a strawman. If the amp is clipping get a speaker with more efficiency or a more powerful amp. Sound quality is not served by quantity if that quantity is also containing annoying distortion products, which are common with a lot of amps without clipping coming into the equation!