If there is one bias that intelligent, technologically oriented people suffer from, it's an over-confidence in medicine and an excessively mechanistic view of the human body. The body is more like an aquarium full of a variety of species than an engine in which a part may or may not function.
Having said that, no one modality is better than the other. Each one has its own place.
There is one more striking difference also between the Western and other modalities and You made it clear by using the word "fix".
For certain conditions, "fixing" does not work. If my arm is broken, sure you can fix it but for chronic conditions, certain lifestyle changes will have to be made and that requires the individual to be willing to undertake shifts in their behavior. For example, what you eat, when you eat, where you eat, how the food is cooked, when you sleep, the ambiance of your work, home and not to mention exercising etc.
So in that sense, the holistic medical practitioner becomes more like a guide and the individual takes on a active role.
For most people, this is too much to do. So they prefer Western Medicine where the mindset is, someone is going to "fix" me while I am busy with my life getting stressed up. The role is passive. Big difference.
It is funny that Western Medicine practitioners are called doctors whereas holistic practitioners use the term heal and are called healers. (The root of the word heal is related to whole)
Now that Western medicine has got most of the low-hanging fruit and is now banging its head on the hard problems, it may appear to fall short in the "what have you done for me lately?" sense. But that's just because we take it for granted that we aren't going to get polio or smallpox.
A lot of Western treatments for chronic conditions aren't that great, but is there anything that's been proven better? It's not exceptionally pleasant for people with sleep apnea to have to wear masks and have pressurized air blown into their breathing passages at night, but at least they get some real sleep. Living with diabetes still sucks, but wouldn't it suck more without the treatments scientific medicine has developed?
[1] "Western medicine" is really a bad name for it. My specific condition was first discovered by a Japanese doctor, hence the name Hashimoto's thyroiditis.
Of course, that's not going to accomplish anything if my immune system has decided to destroy my thyroid gland, or if a stray gamma ray or two has turned a lump of otherwise-useful tissue into a malignant tumor, or if my breathing passages are shaped in just the right way to obstruct my breathing at night.
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.
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.