" against the
fact that all people with such a biological capability will
almost certainly experience a significantly higher rate of cancer. Because in a nutshell cancer is uncontrolled proliferation while regeneration is controlled proliferation."
Almost certainly? Where do you get this certainty from? There is no obvious reason why we should expect regeneration to be potentially carcinogenic, only because both are proliferations. Claiming it as a fact is way, way beyond what science currently knows.
There is an assumption at your end that controlled proliferation can easily switch over to uncontrolled one, but real natural phenomena don't seem to indicate that.
Axolotls live about as long as dogs and cats do, but unlike them, they rarely suffer from cancer.
We humans are capable of regrowing our fingernails and toenails for our entire life and we indeed regrow them all the time, proliferation taking place 24/7, nonstop. And yet cancer of the nailbed is quite rare, much rarer than other cancers, though not completely unheard of.
Our own children proliferate their cells like hell, growing twentyfold in the process, and yet pediatric cancer is not very common, with only 1 of 300 to 500 kids getting cancer before their 18th birthday. It is much more common in elderly people whose cells don't proliferate that much anymore.
You have no real observations to ground your certainty in, it is purely speculative, and this is not maths, this is biology, with all its glorious mess. Even very smart people usually get their speculations wrong when it comes to biology.