I assume that this is far from unique to humans, but not quite universal. I wonder whether the "immortal jellyfish" turritopsis dohrnii has some telomere rebuilding mechanism for all cells that provide its age-defying abilities.

I also wonder whether there is a second advantage to telomere depletion; reducing the instances of organisms from different generations carrying the same genes competing for resources. After all, we're here for the benefit of our genes, not the other way round.