Liver transplants can cost $700K to $1M+. In the US, insurance (or Medicare) typically engages in a special negotiated contract with the hospital. This amount is too expensive for a hospital, or even many affluent individuals, to pay without insurance. (I'm sure there are exceptions for the exceedingly rich.)

For me, a magical additional insurance policy appeared in my hospital account to which all transplant-related expenses were charged.

In addition, to get an organ in the US you must pass a series of exams regarding your physical and mental health, diet, your ability to get post-transplant support, and your willingness and ability to take care of your new organ. Alcohol and drug tests as appropriate. And for these evaluations, money can only indirectly help you.

I would also guess that there is a correlation between those people who have insurance and those that can pass the transplant evaluation, though that's a hidden variable that the powers that be probably want to stay hidden.

Organs are just too scarce to waste on a person who will squander one. It's a life and death competition between patients. It's horrible to see the people who get left behind, who wait too long, get sidetracked by some "miracle" cure, or even happen to live in the wrong region of the country where organs are scarce.

But the true miracle of a successful transplant is almost unfathomable (and that's said by a rationalist). From death's bed to walking a couple kilometers in a month and a half.