I've been mulling over this for a time, and maybe this is not correct.
Is read noise fixed or or random? I suspect the latter, and in fact this is exactly what "skipper CCD''s" utilise by being read-up hundreds of times to get read noise to sub electron levels.
Further, if read noise were fixed, you'd see a gradual pattern build up after summing multiple frames. To date, I've not seen that happen even after summing dozens if frames.
Assuming then read noise is indeed random, would not the noise reduce by the square root of the number of subs.