New technology typically goes through a phase where it is really expensive when it is first released, and then it gets less expensive, right? The Jigsaw Man is set in that initial timeframe. Breakthroughs in the medical science gave doctors the ability to transplant every organ except the brain and spinal column, but the cost was still very high and only a few could really afford it.
Niven does explore the next phase, where the cost comes down (or the technology is replaced by something less expensive), in his novel A Gift From Earth. I think the novel was written before the story, in fact.