With all due respect, I do not see where the Pope is throwing subsidiarity under the bus. One might, for example, look at the situation in France. It’s about 2/3 public and 1/3 private. The central government’s part is pretty spartan. Among other things, you pay up front at the point of service and receive reimbursement from the government (partial-usually about 80%) There are also local governmental authorities which provide for those situations where people can’t, by reason of poverty, do that. So, “universal” health coverage, even “governmental” coverage does not necessarily violate the principal of subsidiarity. Depends on what one means by “governmental”. Presumably, the more local authorities have better knowledge of local conditions and the locals themselves than does the central government.
In France, the private system is essentially unregulated. People have insurance as they choose or pay because they have the money themselves.
But if we’re trying to reach 'universal access", there are a lot more things that could be done besides federalizing the entire thing. In France, the government pays for medical education and malpractice insurance, so doctors do not have to charge twice what it takes, or more, to actually deliver the service. Nor do they have to pay clerical help and programs to be able to bill the government the way our governmental systems require. That particular part is delegated to the individuals themselves.
Medical schools are expanded to meet population needs. Our physician numbers are totally controlled by the universities, which have major disincentives to produce more doctors, and never do produce enough. How many of us know young people who would have made fine doctors, but end up going into some parallel related field because they can’t get into medical school even with excellent grades and test scores? Just about everybody knows such people, I imagine. I certainly have, and do.
Our universities also control the production of NPs. Those programs do not graduate nearly enough NPs, and have some strange requirements (like thesis writing) that have no relationship with providing quality medicine whatever, and which physicians themselves are not required to do.
Craziness abounds. It’s not all about creating some gray socialist system. We ought to be able to do better than that if even the French have.