This whole interview conveys some very strange ideas about evolution. So while I am not able to answer the question directly, I'll hope to make clear why the presented argument is on shaky grounds and hence one does not need to accept Austin's conclusion because of that.
Let's begin with Robin Austin defining what cancer is:
I have two answers. One is it may be due to a fundamental, general instability in any
system which has mutations going on where you’re reproducing yourself.
There’s a fundamental danger there. It’s the risk that the system is
willing to accept in order to evolve.
A system is not willing to "accept" anything in order to do anything, let alone "to evolve". There is no need for livings being to evolve, no goal to be achieved. All we know is that they do, hence the variations of life.
It's true that due to the imperfect replicating process errors can lead to sicknesses, yet a necessity for such a system to be prone to cancer does not follow. There are multiple different genetic defects, why should cancer be special and intrinsic to the process?
It may also be plan B in the sense that we’re supposed to age and die.
It’s very important that we die. If you take good care of yourself so
the normal ways of death don’t happen, the system will go ahead and
turn something else on to make sure that individual ceases.
We are not supposed to do anything. Living beings simply are. We humans tend to search for meaning where there is none to be found and this seems to be one example of that.
It's neither important nor unimportant that we die. Importance is quite a strange concept to apply here.
Living beings are until they die. If they procreate before death, then their offsprings simply are, too. And what stays around, stays around. No need to die, unless you assume that evolution must happen, and that there never could occur a constant state, like a planet only being inhabited by one big immortal plant covering its entire surface.
There is no evolutionary pressure that forces livings beings to gain immortality, but that doesn't mean the individual must die within a certain time frame. (In fact, Turritopsos Nutricula might as well have evolved into something that can be deemed de-facto immortal.)
So to say that cancer is our body's mean to ensure that we die because we must die does not follow. It sounds like an ad-hoc rationalization to make sense out of a (meaningless) sickness.
It's like saying we were supposed to die of bacteria. And by that logic, the invention of antibiotics would have been a bad thing.
Furthermore, we eliminated a lot of other threats which would have killed us in the past, so there isn't much left to kill us. One remaining candidate happens to be cancer. And car accidents. And smoking. Would anybody claim that driving a car and smoking would be "the system's" means to ensure that we die someday?
TS: So, cancer is a way of killing off individuals to support survival
of the species, like programmed cell death kills off certain cells
within the body to support survival of the organism?
RA: Yeah, it’s apoptosis on a large scale. That’s why the immune
system gives it a pass. In fact, the body might even fight your
attempts to reverse the process, because it actually wants it to
Evolution does not work on the species scale. Quite frankly, the individuals of the same species are their own worst enemies as they primarily compete against each other for living space, food, and mating partners. Think about a lion killing the cubs of a lonesome lioness. If evolution would favor the species, how would that have evolved? If we only look on the individual case instead, there would be no paradox.
So the individual is the agent in evolution (or more precise, as Dawkins famously argued, the selfish gene. Yet genes do not occur lonesome on this planet anymore).
Natural selection determines if the individual is fit enough to procreate in a given environment. Each living being has to procreate for their genes to "live on" or where that is not possible, (e.g. a working bee), ensure its closest relatives to live on.
TS: Are you saying that cancer is ultimately good for us?
RA: Yeah, on a species level. We all know that to evolve, we must have mutations. Cancer is more prevalent in humans, because that is the mechanism driving our rapid evolution.
To say cancer is good for us on a species level is as valid as to say "the wolf that caught a slower deer is helping the deers as a species". By that logic, the caught deer must be thankful for being caught and eaten.
Yet the wolf has no intent of helping the deers as a species. It needs food to survive and does so by hunting. It happens that while hunting the wolf most likely will only catch slow and sick animals, while the others more often will escape.
Same with the cancer. It most likely "wants" nothing. It simply occurs due to "defective" genetics. Would anyone shout at the diagnosis of cancer: "Oh joy, I have cancer. My body wants to kill me to enhance the human species. How nice of my body!" I do not think so.
The damning thing about cancer is that there is no evolutionary pressure against it, as we develop its fatal symptoms mostly in our adulthood and it kills its host in relative old age long after it most likely has reproduced. (Or to say it differently: We humans did not evolve a resistance against cancer for the same reasons dinosaurs did not evolve resistance against big comets hitting the earth.)
So, is cancer a trade-off to allow for faster mutations? I do not know. Yet it is just as well conceivable that cancer occurs because of harmful mutations without any benefit from it.
(That isn't to say that there aren't some mutations that hinder old age, yet can be deemed beneficial in the sense that they allow humans to live long enough to procreate in the first place, like sickle cell anemia that lowers the risk of Malaria.)