It's a very good question. Why does anything take a vessel?

With demons, they seem to have a desire for earthly sensation because they used to be human.

With Angels, and also with Vengeful Spirits, it's because they want to affect things here in material existence. So maybe the reapers are trying to have more of an effect on the material world. Maybe they want to be seen by humans, who unless they're near death, otherwise can't see them. As bounty hunters, maybe they can't track the living in their incorporeal forms. It is a good question. :)