The key difference between "Western" and "Eastern" medicine (to use the caricatures) is that Eastern medicine, including traditional practices from all over the world, is person-to-person, while Western medicine scales with technology. Scaling and technological selection allow specific diagnostic techniques and interventions to be optimized through clinical trials, and for cost-effective therapies to be iteratively improved.
That is in fact the best possible way to optimize average healing, but to do so one must average-out individual differences. This process is so well-understood I don't need to explain it here. I want to emphasize instead what is missing from the averaging approach: the thousand informational micro-signals which an individual human emits, such as vocal tone, posture, affect, facial expressions, pulse rate, intra-muscular vibrations, and so on, which together constitute our native communications channel (or "interface protocol"). Those signals can be detected very sensitively by another resonant human nearby.
Such people are "healers" in the traditional sense. Even if every potion they prescribe is snake-oil, their diagnoses based on vibratory cues could be legitimate, and their touch and voice could in fact transmit healing vibrations. As long as humans are vibratory beings, both our maladies and our cures can be vibratory as well.
Perhaps the gravest error introduced by Western medicine is our learned aversion to discomfort. In a natural environment discomfort is inevitable, but at least one can learn from it. When discomfort can consistently be avoided, problems can arise. For example, a person under Western medical advice runs the risk of reacting to (temporary) muscular soreness by immobilizing the joint or region, thereby reducing the short-term pain but increasing long-term discomfort by depriving the joint of practice it needs to stay in calibration and stay supple. In this view most muscular pains reside not in muscles but in the software controlling them; for those cases immobility is the worst thing one can do.