Farm animals are a source of hides, entrails, intestines, meat, bones, as well as milk and wool (some of them). But most of the stuff you get from them is close to useless.
Domesticating animals should be the equivalent of gardening herbs. Let me explain.
Early game you go foraging to gather herbs and mushrooms. If you develop your gardening industry properly, you never have to go forage for those specific herbs and mushrooms ever again. Not only you can produce large quantities of it, but they easily and quickly raise in quality, making it a way better source than foraging. This doesn't make foraging useless, since there's stuff you can't garden, but it does reduce the need for it.
Taming wild animals should have the same effect on hunting.
Farm animals should be a good source of animal parts, replacing the need for "bulk hunting". Hunters would only need to go hunt for specific animals (for crafting specific items), or for bigger prey like marine animals, cave dwellers, or mammoths.
Unfortunately, right now this is impossible.
Animals are a necessity due to wool and milk, but other than that they are close to useless. Their meats (except pork) are among the least used in good recipes. Even after months the quality of their parts will still be lower than the average hunted animal, making it worthless for crafting and not even good enough for quality mulch. And their hides have no special use.
To improve them I think there's 3 main factors:
1st. There need to be good crafting recipes, like equipment/gildings but also food or other items, made with domesticated animal hides to make them relevant. They shouldn't replace ALL other equipments, but at least a few.
2nd. Their generic parts need to be good for something. This either means making them grow in quality faster (and/or more consistently), or make their parts count "more" for specific things (eg. domesticated animal parts could count as twice their quality for mulch production). Because even if we had a great bull cape, you won't be crafting hundreds of them.
3rd. When tamed, their quality shouldn't drop down to 10. This would keep taming relevant for longer, as hunters could bring back new animals from quality spots. The new quality doesn't need to be 1:1, but taming a higher quality wild animal should provide a good quality domesticated one.
We begin as naked beings in the woods, relying on wild stuff to survive. We build villages, with mineholes and wells, to take control of resources and improve the quality of what's available in the wild. We need to be able to do the same with the animals, making hunting something you mostly leave behind as you progress.