I think this is clearly false for humans. I think it is unquestionable that kids do better when parents have actively involved grandparents in their lives. Raising a kid without a support network is overwhelming, and even more so in modern culture where so many kids are raised in single-parent homes. If you measure success of a lineage over time, having the grandparents die off before they get grandkids would have significant adverse effects.
Grandparents sure, but great grandparents? Great great grandparents? I think at a certain point additional surviving generations would be either a neutral or even net disadvantageous change for the greater population. Assuming 20 years per generation, there wouldn't be a huge pressure to live longer than 60-70. We clearly didn't evolve to naturally live forever.
