Age-related diseases and dying from old age is the tip of the iceberg. A much more important part is how the behavior/personality changes with age. We start out foolish and energetic, trying things out, making mistakes and creating new neural connections at the peak rate. Towards the 30s, we slow down, rely more on experience, most of newly learned things are recombinations and abstractions on top of the things learned earlier. Once we approach the end of the life, we become much more risk-averse, hesitant to wander off known paths, and grasping fundamentally new concepts becomes nearly impossible. Remember making fun of all those pensioners still using dial-up?

It is likely related to the limited capacity of the human brain and I doubt it could be easily worked around. Generational change and the limitless supply of the generation Z, willing to break things and learn from their mistakes, is what propelled humanity out of the caves and made civilization possible. I don't think killing it off in the name of abstract longevity would be a wise idea...