You're completely correct, but we take that further in modern medicine. We synthesize, adjust and target particular drugs, even though they might have originally stemmed from "natural" sources (as if some molecules are natural and other aren't...) so that it is more effective for particular use-cases. Treating penicillin as traditional medicine is being disingenuous, considering traditional medicine also "prescribes" keratin from rhino horns as useful...

My point is that generalising both traditional medicine and "western" modern medicine misses the mark. Treat everything on balance, specific to the medicine in question, not the class it came from, in my opinion.