Mikael Risedal wrote: not the well capacity but the QE
No Mikael, not QE. QE is measured in %. Even if you have a 100% QE, the DR is still limited by the amount of light due to its random statistical nature. In the absence of the read noise the smallest signal with the SNR > 1 is 2 photons. The fact that many overlook is that even this small signal has its own photon noise of 1.4 plus the photon quantization noise of 0.5 for the total of 1.9 < 2. Therefore the DR is limited by the well capacity normalized to the number of photons. Specifically, in the absence of the read noise, DR = Log2(Well Capacity / 2).
That would be correct if we only had one photosite and one exposure. But then we would not know the amount of noise. In fact in that case we also would not know what the signal was
Images (in our eyes, in our raw files) are created by sampling Luminance from the scene, the signal, at a high enough sampling rate for the desired level of detail retention and converting the result of the samples to digital units. The sampling rate is given by photosite pitch. We determine properties like signal, noise, SNR and DR by measuring the statistics at the output of a number of these photosites in a patch of uniform signal (the bigger the better).
Luminance from the scene for a given Exposure corresponds to a number of photons per unit area, say about 10 per photosite. But in fact because of the uncertainty inherent in quanta of light some photosites may see 13, some 9, some 7... etc, as you suggest, according to poisson statistics. Ibnformation theory then tells us that the signal is the mean of these values, which could very well turn out to be, say, 10.395. If the sample were large enough that's an accurate representation of the actual physical signal arriving on top of the photosite. Not 10, but 10.395.
Next the photons go through the filters on top of the photosite and hit silicon, producing photoelectrons with, say, an average probability (effective absolute QE) of 15%, also according to poisson statistics. We simplify and say that from a signal of 10.395 photons we get 1.559 photoelectrons (or e-) with shot noise and related SNR equal to the square root of that, or about 1.249.
Next we compute read noise. It also is not an integer, if not by impossible chance.
So as you see QE does enter the equation and in the right conditions the signal effectively comes in floating point notation

So we could very well have physically real values with decimal places and less than 1 (photons, electrons, SNRs). The issue is only whether we can measure them precisely with our equipment (ADC), and that depends on the amount of noise present in the system: we need just enough (for dithering) but no more. The sweetspot these days seems to be a noise floor of around 1 ADU.