Otherwise people would just abandon the horse, forcing the town to pick up the cost of disposal?
Perhaps, but I have to wonder how often horses dropped dead in the middle of the city. Can you be riding a horse into town to pick up some corncobs for the outhouse, and the horse just decides to die?
And people were just walking off and it became a town nuisance? Dead horses everywhere with no one to bill for picking the carcass up?