> There is, if there were no advantage a whole lot more species would die immediately after reproduction like the octopus.

I didn't just meant extending lifespan, I meant extending the time an individual is fertile.

> The utility of genetic diversity puts a lot of pressure against this.

High levels of elitist selection lowers diversity and can have a negative impact on a population's adaptive ability, but there is a sweet spot to diversity. Maximally diverse is just noise after all.

A small amount of elitism is generally what you would expect to be selected for, and we certainly see this other forms in most creatures, but never in the form of extended life span. That makes me suspect there's probably something fundamentally difficult about extending an organism's lifespan given our biological architecture and that's why evolution has favoured other forms of elitist selection.