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It's like high-tech bloodletting with more research and a better track record.
Bloodletting is a theory-based approach and was, as far as we know, in continuous use for thousands of years despite being ineffective for almost every single condition.
The key difference is precisely the research and constant refinement, not any particular mechanism of action.
For example, Colon cancer has a 1.8% success rate with Chemotherapy and Lung cancer has a 1% success rate.
That is pretty abysmal research.
Cancer is the result of DNA damage, which you can get from viruses, chemicals (of all types), sunlight, and even background radiation. Plus, I suspect, random errors in DNA transcription. That's why your body has multiple overlapping systems to detect and destroy cancerous cells.
The idea you'll never get cancer if you just eat right and exercise is a fool's hope - if you don't die of something else first you'll get cancer.
And yes, chemo isn't ideal, but it will normally stretch your life out some. It's certainly not the best we have in all cases - there are targeted drugs for some cancers now.
Modern Chemotherapy isn't someone just presuming something works through informal testing, void of any understanding of the fundamental mechanism by which it works.
It is a necessary evil. Chemotherapy is more akin to amputation of irretrievable mortified flesh than to blood letting.