I'd question that assumption-- each switch in our "genetic configuration" is set to a value, and it's set to one that results in survival often enough for the species to reproduce, but it's not necessarily the optimal value, or even a particularly good one. It's just one that happened to be able to survive under environmental pressures at some particular time.
To put this into a computer science context, genetic algorithms have the same problem-- they can find local maxima easily, but can have difficulty (depending on the nature of the search space) locating global maxima because they can't sacrifice short-term fitness to gain long-term fitness.
Interesting idea, but does the risk of cancer have that much selective pressure? It tends to be the "last thing that kills you", after you live long enough to survive everything else. So it seems like any increased risk of cancer would have to be pretty high before it traded off against injury recovery. Then again, "injury recovery" might not have been as beneficial either -- the time to regenerate would still leave you vulnerable, so adaptations favoring avoidance of that injury would have a leg up in selective pressure.
According to evolution (which hasn't yet noticed medicine), if something rips off your foot, that's not an injury, you simply bleed to death or die of infection even if you win the fight - unlike, say, various small regenerating lizards. What selective pressure could there be to regenerate feet if there were almost no (alive) people with missing feet until the last few hundred years?
However, risk of cancer is serious selective pressure even with short lives - e.g. https://en.wikipedia.org/wiki/Devil_facial_tumour_disease. Cancer tends to be the "last thing that kills you" exactly because so much of our biology is tuned to resist cancer. Also, all kinds of mechanisms causing our aging problems seem to be simply evolutionary adaptations to resist cancer by limiting cell division.
OTOH, cancer rate is probably superlinear with respect to error rate, so a small loss of cell instruction robustness corresponds to a disproportionately shorter lifespan.
That's a false premise.
Plenty of (four-legged) animals can survive just fine without a leg - in fact, it's often said that animals have a spare leg. Some animals might even gnaw their own leg off it's stuck in something and they can't get it out.
A missing foot is survivable for a lynx much more so than for a human in the absence of modern medical care.
The same applies for evolutionary pressure in the case of hypothetical regeneration. A lizard can take ~2 months to regenerate a limb, for a human it would take longer simply since the limb is larger and needs to grow more. Prehistoric humans and hominids were calorie limited - if an injured individual is capable and likely to (a) survive for e.g. half a year with the injury and (b) to obtain much more calories than normal to rebuild many pounds of tissue, then apparently there is no strong evolutionary pressure to favor regeneration it as he/she is capable of procreating almost as well even without this feature.
You're assuming that's the default state, rather than the result of millions of years of cancer-preventing trade-offs. If e.g. being able to regenerate lost limbs gives you a 10% chance of dying of out-of-control cancer before reaching breeding age, that trait is going to be selected out fairly rapidly.
At least for most normal healthy males, not dying prematurely of cancer means you've got probably 50 or so years to pass on your genes. If a cancer causing mutation kills you at 30, you may still have the chance to pass on your genes, but you're still being outcompeted in the larger gene pool by those who don't die early and have more children than you. And if not you, then your children who die prematurely may not procreate. Evolution doesn't really have much noticeable effect at the scale of single generations anyways.
The lifespan of of the axolotl is 10-15 years. I'd love to see the cancer rates for 71 year old axolotls.
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.
Someone would have had to examine a lot dead animals of various species to figure this out.
Least awful sounds more correct.
Then it would be great to be able to turn regeneration on, for that limb only. Any added risk should be much smaller than the always-on version.
Advanced genetic engineering can be used to ensure that particular genes get activated only in the presence of some molecule that isn't naturally present in humans, so it would happen only if you take that particular drug; but it would still be applicable only to "newly built" humans e.g. as part of in vitro fertilization, not as something that can be applied to adults.
It could be those genes raise chance of cancer everywhere. Not just limbs.
A reasonable default assumption is that each switch in our "genetic configuration" is set to a quite good value.
The only exception is if we see a feature that is beneficial at a high calorie cost - those features have been (reasonably) optimized away during our evolution, but would be useful in modern circumstances where food is not scarce anymore; this is a tradeoff where it would make sense to just turn the dial way to the right from where it had been throughout the last million years.