I don't know if sleep apnea has been studied in relation to airplane accidents, but it is clearly a major risk-increasing factor in automobile accidents.
Sleep Apnea Doubles Car Crash Risk, Study Shows
patients with sleep apnea are three to five times more likely to be in a serious car crash involving personal injury.
The association between sleep apnea and the ris... [N Engl J Med. 1999] - PubMed - NCBI
There is a strong association between sleep apnea, as measured by the apnea-hypopnea index, and the risk of traffic accidents.
Automobile accidents involving patients wi... [Am Rev Respir Dis. 1988] - PubMed - NCBI
The patients with sleep apnea had a sevenfold greater rate of automobile accidents than did the subjects without apnea
Seems if there is a medical condition that increased the risk of traffic accidents by 3X to 7X, the FAA would be well advised to look for it in airplane pilots as well. We require pilots to be far more trained, rested, responsible, medically healthy, etc than we require of auto drivers - too late to complain about that. Why treat sleep apnea differently from other medical conditions?
Maybe for a private pilot flying alone, there's not as much reason to care if he endangers himself (the odds of a light plan crash hitting anyone on the ground is really low). Maybe so for private pilots generally, since they usually only endanger their family and friends. But for any sort of commercial pilot, especially the guy upfront when I am in row 23, I don't see what is wrong with this action. And I wonder how many it will affect, anyway. When is the last time you saw a 300 lb airline pilot?