The size of radio antenna should be the same as the size of the radio wave in order to make radio transmitting over a distance of many kilometers possible. In acoustics this is exactly the same.
If the acoustic wave length is much bigger (the low E string has a frequency of 82Hz and a wavelength of 4m!) than the size of the guitar there will be no sound transmission.
At frequencies of a few 100Hz (the D string) the guitar box starts to radiate serious energy to the far field there where the audiance is, 20 meter away from the stage).
The battle of bigger archtops which starded in 1930 and ended with the 19" Stromberg does make sense. They project over a large distance and keep their bottom.