I think Hohohobumperlicious makes some good points. The process of organ donation is perhaps not transparent enough and we shy away from talking about these things as a society. Individuals may wish to donate their organs on their death, but often grieving families will veto the wishes of the deceased, perhaps because they don't want to face it at the moment when their grief is most acute.
My father had fantastic treatment in hospital and we were put under no pressure to switch off his life support, but sadly, we had to take that hard decision. The undertakers were still able to make his body look okay, I believe that organs are removed from a corpse and disposed of as part of the enbalming process in any case. Better that they are giving life to someone else rather than going into an incinerator. We understood the positive impact his organs could potentially have on the lives of very poorly people and their families. We knew that it would have been his wish to help others as he talked about it.
If you are on the register, it is very important to be clear to your nearest and dearest about your wishes, even though death can be hard to discuss. As the early phases of grief ebbed away, we were comforted by the idea that the untimely death of my father helped others.
The OP does raise an interesting question and I do see where she is coming from, but it is unworkable, and I believe that very sick people on the transplant list should be treated with compassion, not judgement at their time of need.