Only legumes used in a cover crop MAY add nitrogen to the soil (temperature, inoculant, pH, etc has to be correct). If you harvest a crop from the field you are removing nitrogen.

For example alfalfa produces up to 500lbs of nitrogen per acre. It needs up to 600lbs/acre from full production. Alfalfa farmers for high production often add 10-20lbs of N after every cutting to make up for this.

The alfalfa is the main crop in those areas of Utah. The oats and barley are rotational crops. This is because alfalfa produces allopathic chemistry which inhibits the germination of its own seeds. So they plant oats or barley to allow the chemistry to break down in the soil for a year or two then back to alfalfa for 5-7 years.