The ability to regenerate body parts and cancer are not inextricably linked. Take the axolotl. It has the ability to regenerate entire limbs. It's also estimated to be a couple orders of magnitude more resistant to cancer than humans.
> Take the axolotl. It has the ability to regenerate entire limbs. It's also estimated to be a couple orders of magnitude more resistant to cancer than humans.
The lifespan of of the axolotl is 10-15 years. I'd love to see the cancer rates for 71 year old axolotls.
There are also many animals who are long living, and immune to cancer (to varying degrees). Naked mole rats live up to 30 years and almost never get cancer (only one case formally verified so far).
Elephants have many more cells than us, and live to almost the same age, but only have a 5% chance of getting cancer, vs 10%-25% in humans. Lions have a 2% chance of getting cancer.