To limit the probability of insufficient clear height over
stairs:
in dwelling units (1.95 m), where occupants are likely to be
intimately familiar with their surroundings, or
in other than dwelling units (2.05 m), where occupants might
not be familiar with their surroundings.
This is to limit the probability of:
persons accidentally contacting the ceiling with their head,
or
persons accidentally contacting the ceiling with their head
in an emergency, which could lead to persons falling, which could lead to
delays in the evacuation or movement of persons to a safe place.
This is to limit the probability of harm to persons.