Whether a population that ages beats out one that doesn't doesn't matter as much as whether an individual that ages beats out one that doesn't.
In the case of a supposed aging gene, consider that genes themselves preferentially want to exist in more fit organisms. If a gene could somehow manage this (i.e. be embodied with more fit genes), it will itself spread. But this is exactly what an aging gene does! Consider how an advantageous gene spreads through a population. This spread is a function of the number of generations that have passed. So a gene that could speed up the passing of generations will increase its own likelihood of existing in more fit organisms (increasing its own fitness), as advantageous genes within the population spread faster and are more frequently "paired up" with the aging gene. But the subpopulation with the aging gene is more fit than the subpopulation without it since the time for advantageous genes to spread is decreased, and so the aging population overtakes its counterpart.
You don't need extra genes or information to prefer organisms that age out of reproductive fitness. If advanced age during reproduction confers lower fitness, then the offspring are automatically less fit. While you could argue that there would be a competition for resources amongst the young offspring, this isn't much different than other scenarios that produce less fit or disabled offspring.
The sharing of genes within a population creates a nice analogy between the population and a single organism. Programmed death for members of an organism is a standard feature of evolution. It's not implausible that such a feature exists at the level of population as well.
https://en.wikipedia.org/wiki/Evolution_of_ageing
None of these has been proven or widely accepted, and the entire class of theories has many rebuttals. They are interesting to consider, though.