It has happened before and it can happen again, although it has sometimes taken centuries to accomplish.
It took two hundred years, from the first effort to vaccinate against it, to eradicate smallpox from the face of the earth, but eradicated it is. Paralytic polio is virtually gone as well. Although tuberculosis has re-emerged as a serious health threat, it is nowhere near the killer it was in the nineteenth and early twentieth centuries, when it killed more than 2,000 out of every 100,000 people in the Western world. Cancer was not much of a problem in those days because people died of these other scourges before getting cancer.
The pace of the current revolution in biology and medicine is really quite astonishing and should reduce the time it takes to make sweeping changes in medicine. It will not and should not take centuries to markedly reduce the impact of today's major killers, including cancer.
The major roadblock to reaping the benefits of this research may well be the ability of our medical system to absorb and translate advances into medical practice, a difficult problem for our cumbersome and economically besieged health care system. Given these complexities of the war on cancer, we should also especially be on guard for the negative influence of the self-fulfilling prophecy. If we believe that cancer can never be eradicated, then it never will be.