I think Jared Diamond had a similar argument that seems valid.
Roughly speaking, it boils down to the fact that you need 90 out of 100 subsystems in your body to be working. Your lungs, your heart, your skin, your brain, etc.
They interact, but each part also needs to work on its own for you to live. Every one of those systems can fail and leave you dead.
Since evolution only "cares" about you to the point where you bear children and raise them, what are the chances that it engineered ALL those systems to last FOREVER?
And then it created a single hormone to control every system and make them stop decaying?
Such a fantastic over-engineering can't occur purely by chance, 100 times over.
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In fact ANY mutation that decreased life expectancy but increased fitness during the reproductive years would be selected FOR.
So it seems possible you have multiple mutations that prevent you from living much longer than "expected".
(I'd even conjecture there's a sexual selection effect going on in the "live hard die young" people, like rock stars, athletes, etc. Their hormones are selected for "living on the edge", and that strategy has proven useful over millenia... i.e. a tendency toward self-destruction is not necessarily something that gets weeded out by evolution)
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That said I think it's definitely possible for some treatment to make someone who would have lived 60 years last until 70, or even 100. It's harder to imagine going from 100 to 200 (especially with productive life).