Doing what you owe the dead, rather than what feels useful or soothing, lets you think about them without regret bending your memories. The strongest reasons for keeping a mourning obligation are the ones that are neither practical nor therapeutic. Skipping it would breed self-contempt that taints every later thought of the person.
A child raised on a creed they later reject still keeps something: the conviction that there is such a thing as truth. A false doctrine taught sincerely can protect a person from the dizziness of believing nothing is true. So one can refuse the doctrine while refusing to mock it.
You can keep a ritual faithfully without believing what it assumes, even when its picture of the afterlife strikes you as absurd. Doubt is not a good enough reason to stop showing up. Once kept, the practice works on conduct: a daily public duty makes the morning's lie shameful by evening.
A fixed year of daily mourning lets the bereaved go on living with the dead, because constant attention to their absence is a way of keeping them near. That is wise at the start, but it makes the year's end frightening: the mourner must give up that closeness and return to the world.
Saying the same prayers three times a day mostly happens through a clutter of distracting thoughts. Then, without warning, the noise stops and only the words remain, and the speaker truly joins them. The daily repetition is what makes these rare moments possible, and in between it fills ordinary life with a music of language.