Empirical research focuses too much on what is published by someone who is "worthy" of knowledge. I am not against it in any sense.
But since you gave a considerable space in your post to medical science I will use that to put forward this.
In India, since thousands of years we use food which is balanced and nutritious. I read somewhere that people in west are having "Turmeric Shots" due to its medicinal properties. That sounds strange to an Indian like me.
We use turmeric in our everyday food.
If you see Indians eating food, most will be in what you call a yoga position while eating food. This proves to actually be good for health. It is a different matter that present India has abandoned its sensible roots and adopted an unhealthy lifestyle.
I am a hypocrite, I am writing this and my sitting position is not what our masters taught us.
The point that I am trying to make is, that there is a lot of knowledge which one can find by an open mind and observing around. It does not need "only" empirical way of research.
My problem with people who "try" (not you by the way) to sound intellectual is that they just disregard a fact or knowledge by asking, "what is your source?".
Sometimes sources are open mind, logic and rituals. I wish for a future where people in research and science have open mind. Open mind to accept and explore everything.
Believe me, if India starts funding scientists to explore hidden knowledge in ancient scripts of India and "intellectuals" in India start appreciating Indian science. This world will benefit largely. Everyone likes Yoga and Ayurveda. That is just one small teaser of what is there to be found.
RE: The Need for Empirical Data in Complementary & Alternative Health