The same fire that will heat your house can just as easily burn it to the ground. Goats are the same way. On the other hand, goats can be hand milked, while for cows you really do need a milking machine. Since we do occassionly work with cows, we have a milking machine, but unless we have a cow, or are milking more than a dozen goats, the machine sits on the shelf. It's easier to hand milk half a dozen goats than to mess with setting up and cleaning the machine.
Goats are very cool individuals.
Left to their own devices, predators would have kept goat numbers down to the point where desertification wouldn't have happened. Rather, I would argue that it was the management practices of two-leggers which led to desertification, and that it's unfair to lay the blame on the goats.