Good point, moish, but that is exactly the issue. Rationing is necessary because every individual thinks that they should get everything that is possible to get. But from a broader perspective, that is not always the most utilitarian choice (not that I am endorsing that point of view).
To give an example of rationing that goes on all the time, think of organ donation. There is a huge waiting list for organs. Hospitals have to prioritize people on the list – so people have to wait, sometimes for a long time, and sometimes they never get. Meanwhile, because of the current thinking in the medical field, the person whose need is the most immediate gets the first call, even if they may have no chance of surviving. Obviously, those people and their relatives think that they should get the organ, but is that really true? Wouldn’t it be “better use” to give it to someone who could resume normal life with a transplant, rather than someone who will be buried with the transplant in 3 months?