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.
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.