So your answer is "let them go extinct"
Sure some wild versions of these animals might continue to survive somewhere, but the common breeds we are familiar with would disappear from the face of the earth, reducing genetic diversity.
And have you considered the fact that a farm without such animals is an inefficient farm and generally requires chemical inputs to keep it running? Animals such as chickens, ducks, goats, sheep, cows, etc do not merely provide meat. They provide many benefits to the farm and I'm not just talking about fertilizer. They also can till the soil (without the use of petroleum products), eliminate weeds (again, without the use of petroleum products), and eliminate bugs (again, without the use of petroleum products)
If those animals go extinct, how do you propose farmers take care of weeds and insects without using petroleum based chemicals? How will they fertilize their soil?