Actually, much of the story would be lost if there were only one narrator in The Plague of Doves.  None of the characters knows the full extent of the history of Pluto and the Ojibwe reservation, and it is only through multiple narrative voices that the entire story comes together.  Cordelia ends up as the town's historian, and she knows about and understands many of the scandals that have happened in town, but even she is ignorant to the fact that it was Warren Wolde who murdered her family so long ago and not one of the Native American men who were accused of and killed for the crime. 

Erdrich writes many of her novels in multiple narrative voices to try to capture Native American traditions of storytelling in her work.  This would be lost if the story were told by only one narrator.

If only one character told the story, it would be a different story simply because of the characters' ignorance of events.  Only an omniscient point of view would be able to render the totality of events in the novel.