Exactly.
I don't understand this popular craving of immortality. If you look at the current society and add immortality, you just get horrific dystopian future, where by the way majority of the world is still mortal just enslaved by power-hungry immortal overlords.
Right now however sadistic regimes are, we still know that Stalins/Kim Jong Uns of the day will die and there is at least hope.
In currently(!) non-sadistic regimes we have inequality issue where richer just get richer and poor get poorer, but at least money can't be taken to the grave, how is it good to eliminate the grave?
And the reasons people usually give for immortality are either outright egotistical "I don't want to die" or a bit veiled "my grandpa/mother/Steve Jobs was a golden person, I wish they still were around".
Well, kudos to him/her, but I take your dead grandpa over suffering of the millions, thanks.
The same for your fear of death, deal with it.
There are some nuances though:
1. We definitely should work on non-suffering in old ages.
2. This grim outlook applies only if there is no other relevant technological revolution happening at the same time. For instance, if we have free nano-machines making everything out of thin air, hierarchy of the society will already alter enough as to allow immortality being thrown into the mix.