April 1, 2017
One criticism of going to a single-payer healthcare system is that it would violate the principle of subsidiarity. Now from the standpoint of Catholic social teaching that is a devastating critique if it is true, since subsidiarity is an essential aspect of the Church’s social doctrine. We cannot simply ignore it. So it is worthwhile to look at both the principle of subsidiarity and the single-payer concept to determine if the two are really in conflict.
The word “subsidiarity” comes from the Latin subsidium, meaning help, support, or relief.  It has a military connotation, referring to reinforcement, or reserve troops.  Applied to economic, political, and social questions, it means that the State is to step in where needed, and not otherwise. Pope Pius XI explained the term this way in Quadragesimo anno:
“As history abundantly proves, it is true that on account of changed conditions many things which were done by small associations in former times cannot be done now save by large associations. Still, that most weighty principle, which cannot be set aside or changed, remains fixed and unshaken in social philosophy: Just as it is gravely wrong to take from individuals what they can accomplish by their own initiative and industry and give it to the community, so also it is an injustice and at the same time a grave evil and disturbance of right order to assign to a greater and higher association what lesser and subordinate organizations can do. For every social activity ought of its very nature to furnish help to the members of the body social, and never destroy and absorb them.
“The supreme authority of the State ought, therefore, to let subordinate groups handle matters and concerns of lesser importance, which would otherwise dissipate its efforts greatly. Thereby the State will more freely, powerfully, and effectively do all those things that belong to it alone because it alone can do them: directing, watching, urging, restraining, as occasion requires and necessity demands. Therefore, those in power should be sure that the more perfectly a graduated order is kept among the various associations, in observance of the principle of ‘subsidiary function,’ the stronger social authority and effectiveness will be the happier and more prosperous the condition of the State.” (secs. 79-80) 
Now what this tells us is that to the extent that private organizations or persons can deal with the problem of healthcare being unaffordable to a great mass of people, they should do so. And the government should not do anything that those private organizations or persons can handle on their own. But it does not follow that the government should not act where private organizations or persons cannot handle a problem on their own. The question does not turn on jurisdiction, but on competence. Subsidiarity is not federalism.
Moreover, the principle of subsidiarity does not require the government to take a hands-off approach even if private organizations or persons can deal with the issue of healthcare in the main. On the contrary, it should stand ready to perform a subsidiary function (from which the principle of subsidiarity derives its name). As the Compendium of the Social Doctrine of the Church explains,
“On the basis of this principle, all societies of a superior order must adopt attitudes of help (‘subsidium’) — therefore of support, promotion, development — with respect to lower-order societies. In this way, intermediate social entities can properly perform the functions that fall to them without being required to hand them over unjustly to other social entities of a higher level, by which they would end up being absorbed and substituted, in the end seeing themselves denied their dignity and essential place.
“Subsidiarity, understood in the positive sense as economic, institutional or juridical assistance offered to lesser social entities, entails a corresponding series of negative implications that require the State to refrain from anything that would de facto restrict the existential space of the smaller essential cells of society. Their initiative, freedom and responsibility must not be supplanted.” (sec. 186) 
So as private organizations and persons go about the business of ensuring that everybody receives needed medical care, the principle of subsidiarity calls upon the government to provide all necessary support. Of course, when it comes to something as expensive as healthcare, a critical aspect of that support is going to be funding.
Now the dictionary definition of single-payer is “a system in which health-care providers are paid for their services by the government rather than by private insurers.”  More broadly, “single payer refers to a system in which one entity (usually the government) pays all the medical bills for a specific population. And usually (though, again, not always) that entity sets the prices for medical procedures.”  But it is to be cautioned that a “single-payer system is not the same thing as socialized medicine. In a truly socialized medicine system, the government not only pays the bills but also owns the health care facilities and employs the professionals who work there.” But a single-payer system can operate without a single medical provider being a government entity or government employee.
So the question becomes whether there is anything about a single-payer system that requires the government to overreach its proper role according to the principle of subsidiarity. It has already been pointed out that funding is going to be a necessary subsidiary role for government, and this is going to be true to some extent under any system. Even now, the federal government provides funding for healthcare for a good many people: the poor and disabled through Medicaid, the elderly through Medicare, and veterans through the Veteran’s Health Administration. And it provides subsidies for many people to purchase health coverage through exchanges set up under the Affordable Care Act. Single-payer would actually streamline and simplify the U.S. healthcare system as it now stands insofar as it involves the federal government.
Another feature that a single-payer system could provide would be the negotiating power to contain medical costs. Currently, health insurers in the United States lack the bargaining power to do that, which, at least in part, explains why medical costs are so high in the U.S.
Beyond funding the healthcare that people receive, and setting the prices for healthcare, there wouldn’t be much else that a single-payer would be required to do. But it is demonstrable that government can do these things better than anything or anyone else. Things that the government probably wouldn’t do as well, such as determining the course of treatment for individual patients, deciding what medicines are best able to treat certain diseases, making decisions about whether surgery is required in any given situation, deciding what doctor people should consult, or whether a specialist should be called in, don’t need to be part of government decision making at all.
And, truth to be told, it is difficult to see how such decisions need to be made by government at any level, even state or local government. As has been pointed out, subsidiarity shouldn’t be confused with federalism, and decisions of that kind made by state or local governments would involve no less of an unwarranted intrusion. Yes, the principle of subsidiarity can be said to prefer the local wherever possible, but, in truth, the most local place for medical decisions to be made is between doctor and patient. It is in that relationship where the human need sought to be serviced can be best assessed.
The principle of subsidiarity cannot legitimately be used to argue against a single-payer healthcare system. There is nothing about single-payer that calls for government, at any level, to reach beyond its unique competence, or engage in actions that could be better carried out by private individuals or entities. Those who argue against it will need to avail themselves of something outside of Catholic social teaching for support.