Cancer is a fairly modern disease. You can even see from the accounts of encounters with native tribes, cancer is virtually unknown until they start consuming western food.
Depends on what we consider "modern". Last I checked, they found cancers on dinosaur fossils. see e.g. https://www.cancerquest.org/cancer-biology/cancer-wild-anima...
As for humans, it is documented back in the ancient Egypt, etc: https://en.wikipedia.org/wiki/History_of_cancer
The hunter gathers tribes we all encounter have very low (if non existent) rates of cancer, diabetes, obesity, and other western diseases. Once they start consuming a modern diet of flour, sugar etc these diseases are now at extremely high rates. You can see this in the aborigines of Australia for example. The inuit of Canada, and so forth.
https://www.nationalgeographic.com/foodfeatures/evolution-of...
Your links about dinosaur cancers said they found cancers only one type of dinosaur. I would say that's a genetic thing more than an environmental. Then the other animal cancers mentioned underneath seem to have a human component involved.
I would say that further supports the theory.
70 is easily a cancer age. Going by the current research at https://scienceblog.cancerresearchuk.org/2015/02/04/why-are-... one can expect 3/4 people over 60 to have cancer. And it's increasing.
So yeah the not living long enough doesn't really hold water. Also juvenile cancers weren't really a thing at all until the modern world (more likely bacterial infections until we discovered penicillin were more likely for juvenile deaths).