David Schraub has a good post about why we should not choose a theory of justice based on its attainability. He says in part,

For example, "nobody should (unwillingly) die of illness" is an unattainable philosophical position -- we probably will never reach a point where nobody dies of a disease. But we can still move towards that reality, by making it progressively less likely that people will die of disease. Someone wedded to the idea of attainability, however, would argue that beyond some point it is no longer unjust when people die of disease -- there is an achievable "limit" at which point the requirements of justice have been met. Demands beyond that are unreasonable insofar as they effectively posit that we can never have a completely just health-care system.

I agree with his theoretical point that justice is more of a process than a destination, as are many other components of morality such as consent and fairness. However, this gets more complicated when we give people actionable rights in morality. For example, bioethics tells physicians that they should regard consent as a process rather than as just an goal to reach, and this is true for a good doctor-patient relationship; doctors should encourage a constant stream of communication that ensures patients understand as much as they are capable of doing and are making decisions accordingly. However, if a patient brings a malpractice suit claiming that she did not consent to a procedure, we have to have a defined checklist of what constitutes consent. We have to be able to say definitively, "At the point the patient received X amount of information and indicated Y decision, she consented for legal purposes." It puts an unjust burden on doctors to give them an undefined obligation enforceable by law.

Or to use David's example of the health care system as a whole, we cannot give people an actionable right to have their illnesses treated to an infinite extent. No system in the world does this; rationing is a fundamental aspect of resource use. The particularly rights-oriented, litigious nature of the U.S. therefore makes legal commentators particularly cautious about saying that something is unjust if it is not stretching for the unattainable. We see this in U.S. law's unwillingness to impose good Samaritan obligations on bystanders; we only make legislation to protect the helpful bystander from liability should his rescue go wrong.