Thanks for the explanation, but I'm not sure whether I'm 100% convinced by the example. Monitoring multiple signals and reacting to them is what machines good at, in fact, a human in the control loop can be a liability for many industrial processes.
Living creatures are not industrial processes. Each one is unique and will behave differently. So while you can draw some generalisations, you can't safely put a machine in ultimate control, or even in a position to provide unreliable feedback. Even industrial processes aren't usually automated in their entirety and usually have 24/7 oversight; "simple" PID loops can misbehave, and this is far more complex with many more variables. The consequences here are death at one extreme and extreme suffering at the other, and so the stakes are too high to delegate it to a machine. This isn't some theoretical problem--a life is literally on the line and machines can not hold responsibility for a life.
Also note that answering the questions of "is the animal conscious", "is the animal in respiratory distress", "is the animal in pain", "are the core reflexes functioning" or "have the core reflexes stopped functioning" all require complex assessment, which a machine can't do. And if any of those are true or false, the complex dynamics make the decision of giving more or less anaesthetic dose a very complex question to answer. If anything goes wrong, it requires intelligent and informed decisions to be made. In some circumstances that includes killing with an overdose for ethical and legal reasons. It would be unethical and cruel to let a machine make decisions of such consequence.
Having another life in your hands is a huge burden. It's both humbling and scary to be given such power and responsibility over another living being, and having done it I'd have to say I find the notion of giving a machine control or even moderate influence over the process grossly irresponsible. Automating every last aspect of our existence is a horrifying concept. Some things need humans in absolute control, and this is one of them. And I say this as someone who eventually became an software engineer for embedded medical diagnostic devices. Think about the ethics of what you are suggesting.
Second, I understand there are very fine details at play. However I disagree with the point that complex assessment is out of a computer's reach, on the contrary, they are especially good at it. I would trust a machine to consider a patients full medical history in accordance with their momentary markers more thoroughly and faster than a human ever could. Not to mention the human factor of being less educated, tired, in a bad mood or simply not available.
Admittedly I know nothing about the protocols in anesthetics, and indeed, it is my preconception there is little more to it than a tight control loop with not much room for wiggle. What do anesthesiologist base their decisions if not data? Perhaps some of the data is not obvious to a machine and we need humans sensors for input, but the thought of people playing god with ad hoc ideas makes me more uneasy than a computer involved. Granted I live in a second world country and capable doctors are few and far between and it must count for some of my bias.