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.
Just using penicillin as an example:
Imagine you have an incurable infection and I told you that there's this mysterious blue mold that, when crushed up and consumed, will cure you. That sounds a lot like alternative medicine, but when you extract the active component and put it in a certain delivery system (i.e., a pill/capsule/tablet) it's "traditional," modern medicine.
> ... traditional medicine doesn't actually heal you.
And penicillin has saved millions [1] of lives.
[1] estimates ranging from "several" to "hundreds" of millions.