When thinking about western medicine and eastern medicine we are comparing a practice that made progress within the last 200 or so years with traditional practices over 3000 years old. This made me think that prior to western medicine there should have been a traditional precursor that was just as comprehensive as Indian Ayurveda and Chinese medicine.
One guess is that perhaps because western healers didn't dare spread their knowledge or were killed due to accusations of heresy/witchcraft by monotheistic religions the chain of knowledge was broken.
Indian Ayurveda and Chinese Medicine also seem to be somewhat linked to spiritual or mythological beliefs of the culture and maybe all ancient medical practices were that way and thus became unsuitable for use by people having a different religious practice.
One guess is that perhaps because western healers didn't dare spread their knowledge or were killed due to accusations of heresy/witchcraft by monotheistic religions the chain of knowledge was broken.
We have a fairly extensive corpus of medieval medical texts, particularly Early Medieval English medical texts known as Leechbooks (leac being Old English for 'doctor'). Old English Leechbooks, the most prominent of which is known as Bald's Leechbook after its owner, are largely collections of what we might call 'herbal medicine', athough they also contain practical guidance for certain diagnoses, surgical advice and guidance on elements of physical medicine (such as treating cuts, wounds, burns and breaks), as well as Classical medicine. Some of the treatments listed in the Leechbook are very much the practices which have entered the popular conception as "traditional (ineffective) Western Medicine", in particular the practice of blood-letting, whether through leeches or by scarification. Indeed, Bald's Leechbook contains Classical medical advice on:
In which time bloodletting is to be avoided [and] in which time blood is to be let
As well as more contemporary advice on things like how to cauterise a bleed, and even instructions on a rudimentary clotting powder.
So what happened to the wider corpus of medicine in the Leechbook? Well, more than you might think became 'regular' Western medicine, albeit in a more refined form. For a small example:
For an infected nail, take a jagged stick, set on the nail with the warts, strike it then so that the blood springs out, then make a thimble and apply old lard over the nail, withhold from moisture for thirty nights. Then take wheat grain and honey, mix together, apply, do that until it is healthy.
Is not particularly different from a modern treatment that lances a potential build-up of fluid, drains the pus, seals the wound and then applies antibiotics. Similarly:
For sudden pain and swelling take wax and hemlock, grind, make into a salve so warm, bind onto the sore.
This, technically, does make a very effective topical painkiller, albeit one which comes with the risk of permanent nerve damage.
Many of the commonly used herbs mentioned in the Leechbook remain important ingredients in 'alternative' Western medicine, particularly plants such as wormwood, plantain, sorrel, nettle and dock.