Excellent point and you are absolutely right. Actually we are probably both right, it all depends what it is being compared. I should have expressed myself better.
On one hand binning reduces the resolution but we get 4x the intensity for each super-pixel as 4 individual pixel get added together, just as you said. The well depth is increased 4x as well and the read noise is 1/4 (am I right about the read noise?).
On the other hand the CFA of the Bayer matrix reduces the intensity of light each pixel sees
when compared to a mono sensor. Red pixel will only see the red light, the blue pixel will only see the blue light and the two green pixels will only see the green light. Note that this is simplification, each "colour" lets a "band" of wavelengths through, see the chart for example
here.
Anyway, the point is that each pixel behind CFA will see less light than its equivalent mono pixel. And I had a mono sensor next to me and could have easily swapped to it
How much less light? That depends on a particular CFA for a particular sensor but I guessed that 1/4 of the intensity will go through (compared to a mono sensor without the CFA). We are not doing the usual Bayer interpolation to extract the colour as we are binning the pixels on the sensor.
Ah, I am even managing to confuse myself now... do you see what I mean? Of course I could be wrong with what I said. Especially the factor of 1/4 between the mono and colour sensor is a guess anyway.