There are animals that don't "age"[1] so of course it's programmed. There's a balance between how often you want to recombine genetics and how long you want to be able to remember. It seems like a better system would have humans decline differently (i.e. no dementia) but having people grow old is almost certainly beneficial to the species.

[1] Their risk of death does not increase after reaching adulthood. I.e. every year after adulthood has the same risk of unexpected death. Humans and other animals that age have their risks of death climb in "old" age.