"there is the potential for each and every cancer to be unique in a significant way."
True, but that does not mean that cancer doesn't have some common root cause. I think that everybody who claims that there cannot be any common cure for cancers should be able to explain two things (you can attack them as well, I will be glad to hear your responses):
A. Incidence of most cancers increases with age in a very uniform way. Like, the slopes of the curves are basically identical for very different cancers. It at least seems that "being young" translates into "being very resistant (though not immune) to many cancers at once, and "growing old" is the magic anti-cure which makes you susceptible for all sorts of cancers at the same time.
If all those diseases were genuinely different, you would expect to see more variation in their mathematical properties. There aren't such close correlations between, say, dental caries and tuberculosis. And if "growing old" acts as a "magic anti-cure", maybe there can be the opposite, too. I get that "growing young" is probably complicated, but I am not that certain if it is categorically impossible in the future.
B. Cancer is not just a human disease, but generally a mammalian disease, but some mammalian species are much less prone to cancer than others: whales, elephants, bats. And what is again interesting, is the fact that the species less prone to cancer are less prone to all types of cancer again, not just a single type or two.
Also, birds don't get nearly as many cancers as mammals do - and again, they get less cancer overall, not just one or two types.
For me, this epidemiological uniformity indicates a possible common root cause, something like "a failure of the immune system to hold bad cells in check", regardless of the vast diversity of the symptoms.
For a rough analogy: people dying of AIDS will succumb to a wild variety of deadly infections, but that does not mean that AIDS is a family of very different diseases. It just means that their immune system stopped being able to hold multiple different foes in check. And once you can stop HIV from ravaging the immune system of the patients, all of these diverse deadly infections are prevented at once.