You really think that humanity is going to selflessly and democratically release this technology for all or even most? You really think that the tycoons of today and tomorrow are going to let an opportunity to "live forever" pass them by? When they can continue to hustle and rule their empires towards perpetuity?
There is going to be an class imbalance, and it will be big, because the formerly cliched topics of life and death are the very focus here: the poor will die, and the rich will live on. It will start fires that will grow out of control in ways we have never seen before. Think of the environmental implications -- you think environmental destruction is bad now, wait until the planet ossifies under a parasitic species seemingly incapable of self-destruction, short of the kind of end-of-the-world scenarios that science fiction portrays.
When I look around, I see an infinite universe. Vertical farming, solar, fission, fusion, astroid belt mining... The list goes on. If there's a glass ceiling it's not in sight or maybe it's after we strip the solar system. If I ask myself what the meaning of life is, it seems to me that we are it. Yees - We should use our resources efficiently but we shouldn't be afraid to see where this thing goes.
Also, people said that about the internet, electricity, whatever. 'Only the rich are going to have it, why would they givee it to the poor?' Cause competition creates pressure to lower costs and sell more people on immortality. However, that argument falls apart if some nuclear powered government monopolizes the technology for the reasons you said above.
It is my hope that anyone who gains "immortality" is quickly assassinated. Death is not something one should be able to run from for very long.