Is there a point in putting eye ointment in a newborn's eyes after a c-section?

Yes: It prevents conjunctivitis in the postpartum period.

State law for some: The acquisition of germs from the female genital tract that could cause eye damage led to this requirement in many states. Even a scheduled c-section has no guarantee that the fetal waters were not leaking before delivery permitting germs to ascend & cause germ transfer.Once acquired the germ may multiply & cause an unrecognized infection over days or weeks.