We don't get cancer so much more than people used to only because of increased life spans. That is, increased life spans can't be the only answer. I don't know much about how life spans have changed, once you take infant mortality out of the equation.
Generally, in the ancient world, people who survived infancy were expected to live into their seventies. Hence, in the Psalms, "The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow..." (Also, apparently, they were expected to live lives of drudgery and sorrow until they dropped dead).
But, yeah, once you take infant mortality out of the equation, we haven't really made much of a leap forward in terms of longevity.
And also maternal mortality - men may have lived threescore and ten, but women not so much, unless you start measuring their lifespans after their childbearing years were done.