There already is; it's called organic chemistry. Completely synthetic medicines are a relatively new thing; for hundreds of years chemists have tested everything they could get their hands on for everything they could think of. Even so, novel natural products are discovered every year, and new uses for them likewise. Even those are usually synthesized, however, for cost reasons. If you find something interesting by grinding up sea sponges or something then you'd better hope you can synthesize it, or you'll never have enough to be useful. Also, if you can synthesize it then you can try a bunch of different modifications to it, and possibly find something similar which works even better. Evolution gives you random scatter-shot of chemicals; it's as likely to miss a really good one as it is to find it. (Plus the sea sponges and algae and so on are all optimizing for their own survival, not biocompatibility with humans.)
The only difference between medicine and "traditional" medicine is that "traditional" medicines are never discarded once they're proven to be ineffective.
The cool thing about the modern way of approaching natural products is that it's reaching far beyond what traditional herbal medicine is able to. Case in point, I heard of a promising new antibiotic that originated from a soil bacterium found in a random grassy field in the US somewhere. The latest edition of Foreign Policy has a good piece on these things.
The origin of that antibiotic is notable for the new method of culturing the soil bacteria in situ, but antibiotics from soil bacteria are not new. Most antibiotics with a name ending in "mycin" were isolated from soil bacteria.
In many cases , the right method to test medicinal properties of plants is to break them into their contituents and test each separately ? and you miss a lot by not doing so(although it is hard) ?
Yes. While most of the components of a plant will have no particular effect, the one component that you're looking for may be lost in the noise. Worse, it could be cancelled out by some other component or components. (Think of proteins which inactivate other proteins.)
The only difference between medicine and "traditional" medicine is that "traditional" medicines are never discarded once they're proven to be ineffective.