A health system is not a public good, access to a physician is both rivalrous (a doctor can’t see two patients at once without degrading care) and excludable. A public good, by definition, is neither rivalrous nor excludable. That’s not to say that the government shouldn’t provide private goods to citizens, but the term public provision or common welfare would be more appropriate to describe what the government is doing in those cases

Agreed, thanks for the clarification.