The original reason that the audio industry was so interested in using dithering was not to increase the effective number of bits, but rather avoid one nasty kind of distortion.
Even in well build audio systems, there are some very low traces of
50/60 Hz hum in the audio signal. In an analog system, this is not audible, since the human hearing (according to Fletcher-Munson curves) drops very sharply below 200 Hz. About 50 dB SPL is required to get above threshold of hearing at 50 Hz.Assuming a low level hum signal in the order of (or sometimes even much less) than the LSB enters the ADC and the hum will produce a 50 Hz square wave in the digital signal and also in the reproducing DAC. Square waves contain strong odd harmonics and the human hearing sensitivity is increased as the frequency get higher. At 150 Hz (3rd), the threshold of hearing is about 27 dB SPL and at 250 Hz (5th) about
15 dB SPL. While the original 50/60 Hz might not be audible, the harmonics (discrete tones) caused by the quantization noise could be very disturbing.Adding some noise to the audio signal also caused the quantization noise due to hum to be randomized and hence much less disturbing than a constant tone.
For instant some of the early PCM ADC/DAC add ons for VCRs that were used in early digital recordings, had a zener diode at a low bias current as a noise source and this was injected directly into the audio signal prior to the ADC.