It is not feasible for a farmer to buy feed during the lifetime of the animal. It’s the reason they have huge pastures for grazing during warm months. During winter they are usually fed hay.
All beef is grass fed period. Some are finished at the end with corn or other dense grains (your soy patties).
Here’s an article from a Meat Scientist.
https://meatscience.org/TheMeatWeEat/topics/raising-animals-...
Mad cow disease propagates from feeding cows the ground up bits of other infected cows.[0]
[0]https://www.fda.gov/animalveterinary/resourcesforyou/animalh...
[1]https://www.cdc.gov/prions/bse/bse-north-america.html
[2]https://www-m.cnn.com/2013/07/02/health/mad-cow-disease-fast...
Visit the Harrison Ranch (on I-5, south-east of SF), and see for yourself how they're treated.