People didn’t live long enough to have cancer back then.
It's a bit of a myth that humans have only had long life in modern times. This is partially due to the calculated "life expectancy" of many eras including infant mortality where perhaps 30% of the population died at age 0. If a quarter or half of your population is dying at age 0, then another quarter or half must likely be living into their 70s for the mean age to end up 35.
Well not really age 0, rather between 0 and 5.
The rest of your point stands.