Nobody around me gives grains to their beef cattle until finishing just before slaughter to give them a bit of fat and marbling. Otherwise they are fed just alfalfa that is mixed with whatever natural grasses and clover and weeds grows along with it in the field. It is pretty much what they would eat naturally and is as close to free to grow as any crop can get. It is half the price of soybeans to buy on market, even less to grow it yourself than soybeans which requires a combine to harvest, and won't cause potential problems like feeding a cow a primarily soybean or grain diet would.

Now dairy farming? I would not be surprised if they feed mostly all grain and beans. Every part of dairy farming is about industrializing both the process and the cow with a lot of selective breeding for ridiculous amounts of milk production. Milking cows now produce over twice as much milk per cow than they did in the 60s and certainly require more nutrients to maintain than a natural cow's diet would sustain. Some cows are producing 10 gallons of milk per day now.