Chemo operates on the fact that we know that cancer is caused by malignant white cells, so what do we do? We nuke all your white cells.
WTF are you talking about? Only a small subset of cancers (known as haematological) cancers are caused by malignant white cells. These are leukaemias and lymphomas. Other cancers are caused by other cells, e.g. carcinomas (epithelial cells), adenocarcinoma (glandular cells), sarcomas (connective tissue cells) etc.
In general, chemotherapy operates on the fact that cancer is caused by rapidly-dividing, malignant cells. Primarily, chemotherapeutic drugs affect the ability of the body to create new cells, often by disrupting DNA synthesis. This means that all cells, especially cancer cells are less able to divide and grow. This is why your hair falls out, you get mucositis etc etc. These are also rapidly turning over cells.
I'm not an oncologist (but I am a doctor, and you'll notice from my spelling that I don't live in the US), so can't quote improvement in survival, but when you base most of your statement around a misleading premise, it makes the rest of your argument look pretty shoddy.