Death is here for a good reason.
There's the general fear of death that drives a significant portion of human morality. If we can't die, we don't fear risking doing things that would result in our own deaths, or the deaths of others. Suddenly we can inflict a lot more harm and give a lot less of a shit what people think, because what are they gonna do, put me in jail for 1,000 years? I'm just going to live for infinity after that...
Aging is a significant source of perspective. As people age, the way they think about their lives change, the way they approach risk changes. Those changes in both thought process and lifestyle are probably one of the biggest contributors to how human societies work. We have probably never had a human society without aging people, so we don't know what a society without their influence would look like.
If people continue to be born, we would eventually run out of space. At that point you reach a new form of political crisis: do you kill people to make space? Do you shuffle them off the planet in rudimentary space stations? Do wars over resource contention increase? Certainly different "seniority" would lead to new social classes.
Death is a necessary part of evolution. If we eliminate death, we have to alter living people's genomes to respond to biological threats, mix up the gene pool, adapt to new problems and somehow try to predict unexpected ones. All of that is currently science fiction; we have no idea if we would get it right, and could end up basically destroying the species from hubris and ignorance. Nature has a pretty good handle on it.
Cultures should change over time, and people need to change with those cultural changes, but it's basically impossible for individual humans to completely change their entire cultural makeup. Can you imagine if people today lived alongside people from 3,000 years ago? We would end up separated not just by nations, but by epochs. It would just further segregate people and cause tension. The world would be so much more complicated than it is today.
Death is part of a process of cultural natural selection. It creates and changes and influences more than it destroys. Entire peoples are wiped out and new ones emerge, languages die and are born, knowledge is lost and created, practices are abandoned and instantiated. Shakespeare was dramatically influenced by death; it's a major plot point in basically all of his writings. Imagine if death simply didn't exist in his world.