I believe the more relevant examples here are the issues facing many low to middle class Americans today. Non-elites are significantly less likely to afford homes, afford marriage at 25, and most importantly in the long run they less power to affect political change. If money is speech, then some people have a lot more capability than others simply based on their bank accounts.
I think a better modern analogy would be lifesaving pharmaceuticals. Unlike cars and cellphones where market forces have driven the price down, in that case we have companies buying IP and increasing the price, since demand for something which can save your life is essentially infinite.
Also you have the problem of where you put this growing population of immortals? It seems that you would have to solve the problem of interplanetary colonization before we'd be ready to solve death.
"It seems that you would have to solve the problem of interplanetary colonization before we'd be ready to solve death."
These things may actually be tangled together. Interplanetary travel is likely to cause some radiation damage to the bodies of the astronauts. Radiation damage manifests a lot like premature aging; these two may have something in common.
In that case, colonizing planets and trying to treat aging will have to develop together, much like development of airplanes and weather forecasting did.