The downside is that you have to move around a lot because your herd always needs new grass, which makes it hard to build cities, unless you are the Mongols. By the way, over the next 40 weeks you will frequently hear generalizations followed by unless you are the Mongols. But anyway, one of the main reasons herding only caught on in certain parts of the world is that there aren't that many animals that lend themselves to domestication. Like, you have sheep, goats, cattle, pigs, horses, camels, donkeys, reindeer, water buffalo, yaks, all of which have something in common. They aren't native to the Americas. The only halfway useful herding animal native to the Americas is the llama. No, not that llama.