Why is 14 a hard limit ? I understand that it's impossible to represent more than 2^14 different intensities but that's not what dynamic range is. DR is log2(saturation point) - log2( blackpoint). Why can't this be greater than the number of bits in the ADC converter ?
It could with a nonlinear ADC, except that almost all IC-based ADCs are linear. So, while the analog DR is the delta between the full well capacity and the noise floor (in e-), a 14-bit ADC maps signal at the noise floor to 0 and signal at full well capacity to 16,383, binning intermediate e- values incrementally, subject to quantization error.
You have the response (possibly nonlinear of the ADC). What about the response of the sensor itself to light ? Must this always be exactly linear ?
Also, if I pool four adjacent signals into one supersize pixel, how many bits do I have in my new "superpixel" ? Do I not have 56 bits ?
That would be too easy, no, when merging 4 pixels you gain (at best) two more bits, because 4 is 2^2 (where the exponent is the one we're interested in). Think about it, you have 4 times a value from 0 to X, so the combination gives you a value from 0 to X*4, which is two additional bits, not X^4 or whatever you need to go to 56 bits! Said differently, you can't multiply the bits by 4 when you multiply the pixels by 4 because the pixels are on a linear, and the bits on a logarithmic scale.