Why farmers use leguminous plants?

Beas and peas and lentils and clover and related cover crops have a symbiotic relationship with rhizobacteria. The rhizobacteria exists in soil naturally, but not in sufficient quantities to produce the nitrogen that plants need. But with legumes used as cover crops, the gaseous nitrogen feeds the legumes, which in turn produce carbohydrates on which the bacteria "feed". When the soil is turned in the fall, the cycle reinforces itself.

Why do farmers use leguminous crops to provide nitrogen to the soil? ... But with legumes used as cover crops, the gaseous nitrogen feeds the legumes, which in turn produce carbohydrates on which the bacteria "feed". When the soil is turned in the fall, the cycle reinforces itself