First if they are sterile how do you plan to breed them? With the exception of the Donkey all sterile breeds have proven too cost ineffective to breed.
As for submissive, we have many breeds sumissive to us. Dogs being one example. Many people consider them beautifull, a few even in rather bizzarre ways. Some species of dogs given oppsing digits and a language which they could physically produce would apparently serve your purposes since there is no mention of sexual conduct. Given the high levels of intelligence in certain breeds of dogs they would be more than capable of some very mundane tasks.
Given other purposes, machinery actually serves as slaves already. With the age of AI fast approaching the intelligence aspect is soon possible. Biomachines include cybernetics may become such. Ole Aunt Edna if she couldn't afford a proper funeral might be forced into the labor force after death or even to work off back taxes. You know the IRS, give them a chance and even death won't stop an audit.
Theoretically our deffinition of what is proper or improper to enslave is based on intelligence. Still there are practical limits. Dolphins have shown a high level of intelligence yet are "enslaved" for performances. This would be very different than the role of dogs which is mutually benificial. Dolphins trained to act as underwater search and rescue would be less of enslavement and more like having a job, however unatural having a job would be to such creatures. As such if the creatures were of limited intelligence then as Humans we would feel ok with their enslavement. We have demonstrated this many times against other human cultures. So much so that no ethnic group does not have a tale of being enslaved somewhere in it's history.
The practical aspect is thus. Machinery is cheaper, more reliable, more controlled and can be better tailored in the forseeable future. That does not mean that bioengineers in the future will not create living machines which will of course last far longer than inanimate objects. The table which heals itself for example. Or that can given a mechanical or dietary stimulus change color, shape, size or texture. This will be real technology sometime in the future. So too will be table diseases. The one and only reason besides the death of your table that you replace such furniture. It will of course have the intelligence level of a plant or less and likely be based off of a plant for it's DNA base. Still the concept is basically machinery. Instead of working in lifeless metal/plastic it is a machine made up of living tissue. We have used bacteria for such purposes for thousands of years. Yeast is one of our most common machines. It creates beer. It raises up bread. Yeast is even used to fuel cars in some places by fermenting fuel grade alchohol. We use insects as a form of insectiside and use cats to remove rodents. So we already use bacteria as a part in a machine. We already use higher animal forms as tools. Getting used to a living table would not take very long.
So the creation of a species, based on humans to me would be redundant. We have machines to remove labor intensive work. We will soon have machines for all forms of pleasure. We are developing machines for dangerous work already. Soon we will have machines which will even think. We have species for comfort and to serve our egos which are already domesticated.
So the only purpose, practical one I can see in the creation of a sub species of humanity is pure intimidation of other humans. Such a sub species before it is technologically feasible to create will be inferior to machines that we can build for all purposes. They will carry a permanent stigma. Then they will be romanticized as is human nature. Given higher levels of intelligence and raised up to be our equal. When this happens those who created/controlled the sub-species would be despised. Revolts would happen and the new species now granted higher intellligence would resent it's method birth creating a species wide complex for thousands of years or more. So in short why incur such a headache?