We eat the seeds, not the blade. I would assume by "eating grass" op meant eating the grass blades. Maybe in the future vegans will genetically engineer themselves to chew their cud. That actually sounds like a cool scifi backstory.
Cow (field) corn is nasty shit, but CAFOs still feed it to cows and use antibiotics to keep them from dying from it. Google Image Search "muddy feedlot".
We don't eat or are able to digest the majority of even those crops. Cows can eat alfalfa which is nearly free to grow and provides free fertilizer for the soil for future rotated crops. Not growing alfalfa would mean relying more on fossil fuel derived fertilizer and increase carbon emmissions from farming.