I'm thinking its more to do with the fact that meat was expensive and takes much more effort to cook back then, not that they were willing to just eat grains and vegetables, likely grains and vegetables were cheap and much easier to cook.

Farmed meat was a luxury in Roman times and game or wild meat was likely also expensive enough to not be eaten every day. We live in different times.

https://en.wikipedia.org/wiki/Ancient_Roman_cuisine/

https://www.historyhit.com/what-did-the-romans-eat-food-and-...

https://www.quora.com/What-did-soldiers-eat-in-the-Ancient-R...

https://www.thoughtco.com/did-roman-soldiers-eat-meat-120634