Just like how only the elites can afford mobile phones and automobiles.
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.
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.