You are invoking an argument that's called "group selection" [1], it's the idea that genes propagate based on whether they benefit the species as a whole. This argument has been heavily criticized and it is not used much in the mainstream evolutionary science. Perhaps group selection has some effect in some niche, limited circumstances but it doesn't seem to be a significant driving force of evolution.

You don't need to invoke group selection to explain dying though. Dying might be an evolutionary advantage, not to you, but to the genes that make you. Which is not the same as the species, at all [2]. Organisms die not to make space for others but because building the mechanisms to keep young indefinitely is not worth the price compared to spending these resources on reproduction mechanisms. Or because the right combination of genes that allow you to have free lunch just wasn't reached yet. If there was a magic mutation that prevents mammals from ageing without any other effects, I'm pretty sure that gene would spread. Quite possibly to the detriment of the species.

(Beware, not an evolutionary biologist, just somewhat interested in the topic.)

[1] https://en.wikipedia.org/wiki/Group_selection

[2] https://en.wikipedia.org/wiki/Gene-centered_view_of_evolutio...