C. Northcote Parkinson wrote about single reports in his 1995 Parkinson's law article published by The Economist[1]. That's the article that articulated in its first sentence the Parkinson's law we all know.
In the article he explains that a worker that feels overworked prefers to have subordinates rather than a peer of his own level that would be a rival for promotion.
A single subordinate is not ideal because the work would be divided between the two and the subordinate would assume an almost equal status in practice. With two subordinates each is kept in order by fear of the other's promotion and the new manager has the merit of being the only one to comprehend the work of the subordinates. This sets the stage for the two subordinates getting their own assistants. He explain how this new group of people make work for each other.
In the article he explains that a worker that feels overworked prefers to have subordinates rather than a peer of his own level that would be a rival for promotion.
A single subordinate is not ideal because the work would be divided between the two and the subordinate would assume an almost equal status in practice. With two subordinates each is kept in order by fear of the other's promotion and the new manager has the merit of being the only one to comprehend the work of the subordinates. This sets the stage for the two subordinates getting their own assistants. He explain how this new group of people make work for each other.
[1] http://www.berglas.org/Articles/parkinsons_law.pdf