Yes but chickens, goats and cows also require food. If all you have is a small patch of ground to keep them on then it would be striped bare in no time. And the food you would have to buy to keep them alive could be better used to feed your family.
a.cricket
As someone who grew up in rural west Georgia, I was already aware of the fact that livestock does need nutrition in order to produce.
And, it is impossible to judge every situation that is going on in Africa.
However, the last thing I would get rid of if I were facing a shortage of corn or wheat would be goats or chickens, which can be sustained of a varied diet.