Edit: perhaps kin selection [1] is the more appropriate one here.
Still, longevity would affect the group and not only the direct kin.
At least in mammals, killing the soma is on the surface such a massive waste of resources that I believe it must be either: (a) biologically implausible to keep an animal reproducing for a longer timespan or (b) caused by mechanisms that are counterweighted by massive reproductive benefits while the animal is young.
How is it a waste of resources? Evolutionarily, the goal is to produce another successful generation who then begets another generation and so on. The rate at which that happens is a balance between what is necessary to confer the best chance of survival to each child, the number of children needed to outweigh the mortality rate, and the required mutation and crossover to adapt to the environment. Keeping the same individuals in circulation longer doesn't confer an advantage to their offspring since they already posses the same genes. It would more likely hinder the propagation of their genes by taking resources away from their progeny and competing for mates, territory, status, whatever.
Small comment on the argument against anti-aging genes existing: "genes only propagate if selected for, and there’s no selective pressure for longevity after reproductive age" (I know that this was just a very minor aside, but I still think it's worth pointing out the flaw.)
That's not how evolution works. Even after you have reproduced, you have impact on whether your children survive and reproduce. This means that there could very reasonably be evolutionary pressure in either direction (causing people to die younger that way they stop taking resources from their children or causing people to live longer that way they keep providing support for their children).