Well the animals will breed naturally while they are on the rangeland, this is typically what happens anyways. You’d have to implement some type of population control if you wanted to maintain lack of population growth. I’m not sure if that’s really what you meant by not breed them.

It’s also not only about the effect it has on the animal, but the effect it has on the climate system as a whole. Managed grazing of pastureland is going to be necessary for the rapid restoration of lands. We can’t artificially recreate the positive effect animals have on the land without using animals themselves, and if we don’t actively manage it then the restoration will not be rapid enough to combat desertification.