I’m going to quibble with the assertion that the principle of subsidiarity prohibits governmetn involvement in healthcare.
For very good reasons (which are another story) the Popes have supported the principle of subsidiarity which, simply stated, stands for the proposition that any kind of human need should be addressed at the most proximate, capable level. So, for example, if an individual can see to his needs, he should not resort to the central government, the state, the municipality, the parish or even his own family to meet those needs. If, however, he cannot, but the family can, the family, being the most proximate capable provider, should. And so on.
Central government involvement is not precluded, but it should be regarded as a last resort, and only if the need cannot be met at a more proximate level.
So, when it comes to subsidiarity, the real question is whether the central (federal in our case) government is the ONLY level at which the need can be satisfied. If uniformity of outcome is the desired goal, then one could argue that it should be. But there is nothing supporting the idea that uniformity of outcome or access is somehow the only moral resolution, or that the central government is even capable of doing that or doing it without creating greater problems than it solves.
Manifestly, the federal government is not the most proximate source of resolution when it comes to healthcare. Some individuals can pay their own way. A proper organization of society would insist that they do so. Some can’t pay their own way, but have family members who can do it for them. (like the child of a wealthy person). Some (fewer all the time, but some still) can resort to parish or community resources. Some can enter into health insurance agreements at a cost they can afford. Some are so devoid of resources that they can contribute nothing to their own care and so devoid of more proximate benefactors that the federal government may be the only available resource.
Therefore, it is my position that a federal “single payer” plan violates the principle of subsidiarity. So, in my opinion, does a comprehensive federal takeover of healthcare in any guise. It is my further opinion that it is morally distorted for the federal government to seek such a resolution; first because it isn’t necessary and second because the federal government is a woefully blunt instrument; third because all governments rely on coercion to accomplish their goals; fourth because (and this is the evil subsidiarity is intended to combat) extremely powerful and remote entities tend to impose their entire culture and morality onto individuals.
Subsidiarity would not dictate that no governmental level should relieve the need of those who absolutely can do nothing to help themselves and have no more proximate resource. The Social Encyclicals are very clear that there is no inherent reason to go “up the chain”, but only when it’s absolutely necessary to do so.
Somewhat fearing to be labeled a Francophile again, my purpose in pointing out that even in a socialist-tending society like France, subsidiarity is better served than what the left in the U.S. intends for Americans. There are other alternatives, and potential mixes of alternatives. For whatever reason, nobody seems to want to explore them. It seems to be "all or nothing’ for many on both the right and the left. I don’t think the Church teaches either extreme, either in general or as regards healthcare in particular.