I have no opinion either way, since the field seems to be dominated by empirical "evidence" and cranks, but this guy's entire argument rests on this sentence:

"One of the myths of "Uberman sleep schedule" is that it makes it possible to enter REM sleep and skip non-REM sleep stages entirely. That myth is derived from another false claim that implies a non-essential role of deep sleep. I will ignore these claims as standing in total disagreement with laboratory findings and models of sleep. Instead, let us focus on a more plausible claim of the possibility of compressing sleep stages.".

I.e. "I will ignore one of my opponent's arguments and instead focus on another. Since I can rebuff the other argument, my original viewpoint is true". It's a logical fallacy.

He also tends to say "X is unnatural/abnormal" => "X is unhealthy".

I wish someone did serious research into the topic without prejudice.