there might be a differential equation that describes a small part of beings (not a "huge number") benefitting from the free energy that diurnal animals might be at night. There's an equilibrium that's clearly preferential to daylight animals.
Point in case, bats as my primary example seem to be pretty archaic, with highly developed specializations, but nothing really highly developed. Which I see as an expression of the low entropy in the dark (the signal to noise ratio for sound is rather good at night though). Deep see animals are mostly outliers inhabiting a niche, as well. Whereas people as the highest developed species, if I may say so myself, don't even quite get along with crossing the day-night boundaries, I don't see your argument at all. You are rather proving the point.
I'm not convinced because your answer doesn't address the nervous activity of these lower animals. Maybe they don't exhibit any at all in that state, but there's no reason to preclude this diffuse, sparse network from exhibiting patterns exhibiting precursors to sleep comparable to at least one of the human sleep phases.