Grains and legumes are also complementary for soil fertility, because the roots of the legumes support symbiotic nitrogen-fixing bacteria which replenish the nitrates depleted by cereal crops.
There are other ways to close the nitrogen cycle, such as seasonal flooding or the terraced aquaponic rice paddies associated with China, but for civilizations based on "dry" farming of cereal grains, crop rotation with legumes was the predominant way of maintaining soil fertility.
Hence why these civilizations all featured staple meals combining grains and legumes.