Dog/Cat food was not a thing until the early world war(s). The "fresh food/meat" had to be reserved for the military so "Dog/Cat food" was created because people still love their pets but couldn't feed them the way they used to. Or at least that is what I have read, I could be wrong and would welcome someone correcting me or adding details.
That sounds very plausible. Old people had sayings like "she's more mixed up than a dog's breakfast". That saying could only be a thing if people were feeding their dogs just a bunch of leftover human food.
Dogs were domesticated by eating the leftovers form early humans. It is not unreasonable to consider that as common back then. Also, I am fairly sure both dogs and cats were fed the raw bits that the humans did not find as desirable.