[1] It isn't actually western, because it's also used in the east, middle-east, south, both sides of every divide, etc... In the same sense, there is no "western chemistry" as an alternative to "eastern alchemy". There's "things that work" versus "things that make you feel slightly better because they're mild narcotics or stimulants... at best."
(I don't want to focus too much on Chinese herbal medicine, because I see the same cargo-culting non-scientific thinking in code development too. I've lost count of the number of times I've seen an n-tier SPA monstrosity developed for something that needed a tiny monolithic web app, but mumble-mumble-best-mumble-practices.)
The Chinese call the practice of truth seeking, in a more broader sense (outside of medicine) just "science".
"Western" medicine is also not merely the practice of seeking universal medical truth. It is also a collection of paradigms that have been developed in its long history. Like all paradigms, there are limits and drawbacks: phenomena that do not fit well. Truth seeking tends to be done on established paradigms rather than completely new ones.
The "western" prefix is helpful in contrasting it with TCM, which has a completely different paradigm. Many Chinese, myself included, have the experience that there are all sorts of ailments that are not meaningfully solved by "western" medicine practitioners, but are meaningfully solved by TCM practitioners.