Before we get to this the meat of the question, we should first address the MUCH more obvious thing to do with Necromancy: extend human life. Instead of putting animals into human bodies, people would generally prefer to extend thier own lives meaning that it is far more likely for your mythical creatures to be bred as vessels for human souls than the other way around. If your body is irrevocably destroyed, a necromancer could place your soul into a soulbeast to keep it from moving on, then if you are wealthy enough, when another human body in reasonably good shape shows up that COULD be used as a vessel for an animal soul, you would then put the rescued human soul into it. Nobility would spend a fortune on such a service meaning that the market value of a human souled zombie would far outway the unit value of an animal souled zombie in most cases.
With this being the case, an animal-souled zombie would need to have a job in mind worth as much to an investor as extending the life of a wealthy merchant or nobleman. Putting an animal's soul into a zombie for plowing a field would simply not be a worthwhile investment compared to putting a rich man's soul into zombie. This means you need to solve one of two problems:
OPTION A: Make zombies for jobs that are worth more than most person's life:
Human loyalty is subjective compared to many animals. If your mythical creatures are breed for loyalty and obedience, then thier souls would make for ideal servants in places where trust is paramount. They would be prefered to human souled servants as bodyguards, royal cooks, tax-collectors, etc. To a king, the guaranteed trustworthiness of the single person who can most easily kill you is worth more than a hundred extra soldiers guarding some remote outpost; so, they would pay a lord's ransom for these zombies. Also, tax collectors in the ancient world were often the richest people in any given town due to the sheer volume of wealth they were able to skim before delivering thier collections to the state. Eliminating this corruption could save a ruler hundreds of pounds of gold and silver per year making the investment in a zombie worth a lot more money than most people could ever afford.
OPTION B: Make zombie-hood undesirable for humans, but not soulbeasts:
When a person dies and another person's soul is put into that body, the body is permanently scarred from the trauma of its death. To live in a body that was once dead is to live in a state of unending pain. Your mythical soulbeasts however are unable to experience pain of any sort so when thier soul goes to live in a zombie body, the soul simply does not register that it is in pain, because it is not designed to understand what pain is. So, while a human soul is tortured to the point of madness by the experience, soulbeasts can use the body to more or less the same effect as a human could use a natural body. In this case, a land owner might keep a flock of soulbeasts so that when one of his serfs dies, he can have a necromancer reanimate it for a modest fee so that it can go on to farm and pay taxes for years to come.