> Given pre-science Europe's high failure rate, why do you believe other cultures will fare better?

That's a very interesting question and I've been thinking about this problem myself for awhile:

1. How do we actually know that there was a 'high failure rate' for pre-modern treatment methodologies (e.g. ancient doctors were incompetent)? There are plenty of stories of specific failures / successes (e.g. finding that the cause of malaria is not 'bad air', or discovering the germ theory of medicine + sanitation), but that is almost a tautology that every 'advance' in medicine represents a 'failure' of past medicine. That doesn't necessarily imply that doctors in the past were grossly incompetent at treating other ailments, especially given the tools available at the time.

2. Was traditional Western medicine, in practice, actually as dogmatic as we might believe, or is this historiography that we tell ourselves about the triumph of abstract reason over faith and received knowledge? Note that empiricism is often the opposite of dogmatism, but here you equate them. And if you have developed a 'dogma' based on tried-and-true empirical experience, then perhaps it's because the dogma works and is actually adaptive?

3. Personal experience with non-Western medical traditions, which are often the exact opposite of 'dogmatic' (e.g. always take this one true remedy for this one particular condition).

Chinese medicine's philosophy, for example, strongly emphasizes taking into account the entire history of every patient, which makes it 1) probably a better representation of long-term health but 2) very difficult to test in a double-blinded, Western scientific fashion because the personal, dynamic relationship between patient and doctor is integral to the entire process, and because the context of the patient is important to the treatment, whereas the 'FDA model' of treatment is a 1-to-1 mapping of 'condition' to 'treatment', with only rather limited ability to account for the patient's context (e.g. by pre-trial screening).

Note that the biodiversity of India, China, and South America is probably an order of magnitude higher than Northern and Western Europe (Europeans literally fought wars to have access to spices, after all), so these cultures have had much more raw material to work with for, say, plant-based medicine that Europeans ever did, and these plants were not just treated purely as medicines but were and still are integral parts of cuisine and diet.

As a Chinese person, traditional folklore of what to eat to cure various ailments is still high ingrained in society, and they 'work' insofar as I've personally felt physically better when I follow those dietary guidelines rather than not. 'Feeling better' is not something that is easily tested, and we even view it with great suspicion as the 'placebo effect'.

Note that I'm not advocating the superiority of traditional medical systems over the modern, scientific Western framework, just noting that the work of truly evaluating traditional medicines scientifically is still in its infancy in many ways, and is highly colored by the cognitive biases inherent in Western culture (preference for abstract analysis over holistic evaluations, mistrust of subjective judgment over 'objective' physical metrics, finding 'silver bullets' followed by widespread industrial deployment (e.g. antibiotics) over personalized evaluations).

Here's one interesting example of a traditional treatment that may fine success [1].

[1] https://www.ncbi.nlm.nih.gov/pubmed/15637565