I always felt like breeding animals added a nice sense of longevity to caring for your farm animals - a long term goal - and loved breeding my cows overtime to produce better quality/new types of milk. That said, even if it were just a cosmetic thing like how Fields of Mistria does it where you just breed to get new colors for your animals, I feel like such a system would bring more interactivity to the livestock side of the farm.
Given that the animals currently available aren't specifically gendered (no roosters vs chickens, no bulls vs cows etc.) it sort of feels unlikely to me, but I would love to be pleasantly surprised!