If if immortality didn't have negative consequences as severe as stunting an entire species, we'd probably see more species that were capable of immortal individuals. Such species do exist, but not in the Mammal kingdom as far as I'm aware.

But I also think it sets a good guideline. Death improves a species, because it leaves room for more children + more generations (for a given set of resources), which means more opportunity for improvements to evolutionary fitness.

edit: another commenter pointed out something I think is fairly profound. When a group of cells in your body decides to pursue immortality, it's usually cancer. And if you don't address it, it kills you, and them too. Science theoretically has a way to grant our individual cells immortality without causing cancer, but it'd have to be orchestrated carefully.