The cancer chemotherapy regimen of a taxane and platinum combination was developed more than forty years ago, yet remains the cornerstone of treatment for several major cancer types today. Although many new agents targeting cancer genes and pathways have been developed and evaluated, none have been sufficient to replace the long-established taxane/platinum combination. This leads us to ponder why, after four decades of colossal efforts, multiple discoveries, and tremendous advances in understanding gene mutations and biology, the development of conceptually superior targeted therapies has not yet achieved overwhelming success in replacing cytotoxic chemotherapy. The concept of targeted therapy is based on the idea that blocking the altered pathway(s) crucial for cancer development (and maintenance), the disturbance in cellular signaling, metabolism, and functions will make the targeted cancer cells unfit and trigger programmed cell death in cancer cells, but without the significant side effects that limit chemotherapy. We propose that the lack of anticipated triumphs of targeted therapy stems from the desensitization of programmed cell death pathways during neoplastic transformation and malignant progression of cancer cells. This renders the targeting drugs largely ineffective at killing cancer cells and mostly insufficient in clinical implements. Recent advances in understanding suggest that, in contrast to targeted therapies, taxanes and platinum agents kill cancer cells by physical rupturing nuclear membranes rather than triggering apoptosis, making their effect independent of the intrinsic cellular programmed cell death mechanism. This new recognition of the non-programmed cell death mechanism in the success of chemotherapeutic agents, such as taxanes and platinum, may inspire oncologists and cancer researchers to focus their efforts more productively on developing effective non-programmed cell death cancer therapies to replace or significantly improve the application of the current standard taxane/platinum regimens.