Not to say that the other reasons for death are not related to mutations. Edit: also I worry I am making a selection bias - presumably extra protection from cancer may be required along with many other traits to become a centenarian (A and B and C …).
Why do you think that?
Death rates for cancer continue to trend upwards by age: https://www.cancerresearchuk.org/health-professional/cancer-...
If your “hypothesis” were correct, the rate of death would decline after the early fatalities occurred.
Because it is a truism. If they lived as long without cancer as everyone else, they per definition are not more susceptible. It's simply a restating of what being more susceptible implies.
> If your “hypothesis” were correct, the rate of death would decline after the early fatalities occurred.
This does not logically follow. This assumes that removing people with a genetic or other predisposition for getting cancer early would reduce the average risk of cancer more than increasing age increases it.
Mortality rates compounds. Reducing your average risk of dying of a given cause by even a tiny proportion on a per-year basis adds up to substantial chances of surviving longer.
Treatments that reduce mutations in general could make the immune system less effective (increasing your chances of dying of disease, and that of passing a disease on to others). It could also cause fewer mutations in your offspring, which might hurt human evolution over many hundreds of generations.
Curing cancer tomorrow, but with side effects of dramatically increasing transmission and deaths by transmissible disease, and causing humans to die out from failure to adapt to future environments seems like overall a bad plan. It's certainly something we'll need to fully understand before making use of.