What animals are you thinking of that can't run? Turtles? I don't think I know of any societies with majorly domesticated tortoises, and they tend to be small outside the tropics anyway. All domesticated animals I can think of can run, even if they look stupid doing so. (Chickens always look silly.)
You do have a point about pigs being omnivorous, and therefore inclined to eat animals, thus shedding blood -- at least I assume that's what you meant by saying pigs weren't naturally herbivorous -- but pigs mostly don't hunt like cats or dogs. They're scavengers. They eat what they find, including their own poop. (ew) Pigs will eat almost anything, including things that are poisonous to us, so they're easy to feed. They don't need to be hunting down things and shedding blood.
Also what Karger said:
Cows are fussy, fragile animals, and goats get into trouble. Sheep, which Karger didn't mention, are just dumb.
Are pigs really that hard to herd?
As for why pigs repel shades:
Pigs hearts are used in our world to study the human heart because they're pretty similar and much easier to get. Maybe there's something unusually humanlike about pigs? And once people think they repel shades, they will because Cognitive nonsense.
Why to keep them instead of getting more people:
They're easier to feed and can be sold. Also, you don't have to pay them.