...Let me add a twist: the ADC works linearly, but what you see is log
So, if you have a 14-bit ADC (you can count up to 16384)and can record 14 stops of DR, here is how those values will be distributed:
14th stop: 8192 to 16383
13th stop: 4096 to 8191
12th stop: 2048 to 4095
11th stop: 1024 to 2047
10th stop: 512 to 1023
9th stop: 256 to 511
8th stop: 128 to 255
7th stop: 64 to 127
6th stop: 32 to 63
5th stop: 16 to 31
4th stop: 8 to 15
3rd stop: 4 to 7
2nd stop: 2 to 3
1st stop: 0 to 1
This is incorrect - if you replaced "bit" with "stop" then it is correct (and it's then obvious why ETTR works too.)
It's easier to consider a 3- or 4-bit digitiser. Let's say it offers 4 bit resolution then the possible counts are 0000 through 1111. This translates to 2^4 or 16 levels. Written the way that Norman stated it, there would only be four distinct levels - this is incorrect (but I understand he meant there would be 16 levels.)
Some things appear to have been glossed over in the discussion. First, the ADC operates on a per-pixel basis.
I've read the DxO tests on various sensors. It is important to remember that the notional dynamic range is referred back to an 8 mp standard. This means that the D800's quoted 14 bits dynamic range is significantly less than 14 bits at a per-pixel level. The 36 mp > 8 mp conversion gains the sensor sqrt(4.5) = 2.1x notional improvement in dynamic range. The 2.1x is slightly more than 1 stop in quoted dynamic range. This means that the true per-pixel
dynamic range is about 12.9 stops.
In order to read those 12.9 stops, the ADC needs a bit more resolution than the 13 bits required by the pixel. I'm quite surprised because the 14 bits in the ADC suggests that the entire detection chain has ~1 bit of noise.... It sounds improbable.
Photon shot noise has been commented on briefly. If we assume 13 bits dynamic range and (say) 10% quantum efficiency (pidooma), then the number of photons required to fill a pixel is 10 x 2^13 or 80k. Since shot noise varies with the square root of the number of photons, the pixel could have shot noise of up to 280 photons (rms).
Since 1 bit translates to 80k/8192 = 10 photons and we must have about 6 bits of photon noise at the upper end of the sensor's dynamic range. At the bottom end, the quantum efficiency sets the performance and there must be ~3 bits of noise.
Shot noise alone suggests that the true dynamic range of an image cannot be more than about 8-10 bits. It seems that the only way to improve on this is by greatly enhancing the sensor's quantum efficiency.
To answer the OP's question - photon noise alone suggests that there's not a whole lot of benefit to high resolution ADC. It does allow for more sophisticated noise filtering - presumably at the expense of resolution.
<---- physicst / astronomer