It is also the final defense against unrestrained cell divison; a natural protection against diseases such as cancer.
There were cultures where the oldest men in the tribe got exclusivity over the teenage girls to reproduce with. Also, since men can reproduce in old age, that sounds questionable to me.
So that people die when they're no longer reproductively viable / relevant, rather than using up valuable resources. Wouldn't telomere shortening have some selection-pressure advantage?