I'm only answering this part, because I also don't want to get involved in a homeopathy debate.
They do look at human malfunctioning as a whole system. The people who do this are called "internists". Your primary doctor is probably one of them.
The reason that there are so many specialists is that the human body is really complicated. As much as we would like it to be simple, there's just too much to know about it for any one person to know everything, even if all the information is available. For the same reason that mechanical engineers specialize in things like mechanism design, aerodynamics, or materials, doctors specialize in different areas of the body. An internist simply does not know enough to figure out everything that could possibly be going wrong with a person's body.
To my mind, the big problem is not with the specialization; it's with the coordination. All of the above specialties, and more, were involved in the design of any given vehicle you're likely to encounter, from a performance bicycle to the Concorde. Yet, it's really hard to get doctors from different specialties to collaborate to tackle a complicated disease. This is not a problem with medical science, so much as a problem with the way things are done right now.
Of course, for very common symptoms (like headache and nausea), they usually just treat the symptom.
I think you should clarify what you mean by homeopathy before arguing that it is superior. I suppose it's possible that someone administering homeopathic remedies may have a belief about the body as a whole, but I think it's a stretch to consider homeopathy an improvement on western medicine in any way.
Though I am not going to start another controversial thread (about homeopathy), I just wonder why the mainstream medical science does not looks at human malfunctioning as a whole system. In other words why there are so many organ/tissues/functions specialists?
May be (with main stream medical science) we are on wrong path and have made things so complicated that it has impossible to consider the whole human body in one shot in any particular disease. Though we fully know that analyzing/treating the parts in a complex system won't take us too far.