Generational warfare would definitely be something to consider. Imagine if immortality had been discovered 400 years ago. Are the ethics and morality of the leaders from 400 years ago something you, a person born in the late 20th century, would want to live under?
Generations eventually dying off keeps the human race moving forward in many ways.
Imagine if we grew up in a world like the one you posit, where humanity advances only slowly because it's held back by the ideals held by people 400 years old.
You propose that the best solution to this is kill everyone over 80.
Or, imagine that you didn't like the dominant views among the 50-60 year olds in power when you were in your twenties, and you offered up the idea that we should just withold medical treatment from people over 30 so that we could increase the speed of social progress.
Generations eventually dying off keeps the human race moving forward in many ways.