The reason cells die is because their DNA’s telomeres reduce in size at every division. Once the telomeres are gone, the cell cannot divide properly leading to an eventual cell die-off. But we already have examples where cells’ telomeres stop reducing in length from cell division.
We call it cancer.
Cancer is when cells reproduce too quickly. If our cells didn’t reproduce at an abnormally fast rate and its telomeres didn’t reduce in length we would simply age at a slower rate, not have cancer.
I have no doubt that the major reason for the 30-40 year lifespans of the past was indeed high infant mortality. But recent medical advances must have lengthened the lifespans of a lot of adults too.
Sure, there were a few people who lived to be 100 in the past. But I’d wager that a lot of people are alive today who would have died before 50 without modern surgery and medicines. As casdave cited, people of 40 in 1900 looked much older than today’s 40-year-olds.
Consequently, there are probably a lot more people living to be even 70 today than in Biblical times.