"What is the benefit of natural chemicals over synthetic chemicals?"
The short answer is that we know nature better than we know the man-made world. The information might not be stored on a computer, but it’s stored in the collective memory of thousands of years of human development.
Both animals and humans have used the chemicals in nature throughout their evolution and have learned what works, what their side affects are, what is poisonous, and how to use them effectively. Synthetic drugs, we’ve only had for about 50 years. Some 100 years ago, aspirin was made with salicylic acid derived from willow tree bark. But around the 1950s it was discovered that it could be made with acetylsalicylic acid derived from fossil fuels (petroleum) less expensively. Animals know that willow has medicinal properties and will eat it when necessary. People have simply come to rely on other methods of pain relief or other symptoms.
Natural chemistry is not easy science, but we do have the ancient traditions of Egypt, China, India, Russia... many centuries of knowledge to learn from. Today there is tough competition in the marketplace between natural dietary supplements and synthetic drugs. I think this is good, fair competition and those natural supplements can be very beneficial for a healthy life.