I've always assumed its spontaneous specialization of species: leaving the safety of their nest at those times of day when they are the fittest to occupy a niche.

Once energy conserving "sleep time" exists, the genome can postpone or schedule for activity during these times of day, if it turns out to be more effective somehow.

Probably because it evolved very early (like before bilateral symmetry, multi layer body cavity, or kidneys early... maybe even before multicellular animals early) and so has been incorporated as an essential pillar into multiple processes layered on top of that fundamental architecture.