I think you're looking at it too narrowly. Kaito was going to die. If not now, off a rooftop in New York, then sometime. It happens to everyone. Well, except, apparently, Adam Monroe.

I think that's what Kaito meant.
Hiro's epiphany most likely came when he realized that his father was not afraid of dying, that it meant he would join his wife in the hereafter. Hiro probably also recalled how he was unable to save Charlie from dying.