I frame the question thusly: Should healthcare be provided as a public or private sector service, is it a right or a privilege, and what level of government should apply.
In most urban areas, fire and police are public services. The electorate has decided public funding is necessary for the general welfare, obviating the free rider issue (at least for taxpayers). Healthcare, on the other hand, is handled as a hybrid: emergency outpatient care is provided by fire departments for example, although they may seek payment ex post facto.
In rural areas, firefighting may be provided on a volunteer basis (e.g., volunteer fire departments) or people may be self-reliant. Similarly, public sector involvement in healthcare is generally less robust than it is in urban environments.
The federal government has taken a much broader role in healthcare than it has in police and fire services, via an unwieldy hybrid at the federal level. There are government-owned and run healthcare providers (e.g., VA, Indian Health Service, military) alongside the private sector. Public payers (e.g., Medicare, Medicaid) parallel their private sector counterparts.
Given the variegation of our nation, a more localized approach to healthcare may make more sense, yet it poses challenges to those lacking means. Conversely, a single payer approach has the merit of simplicity and the purchasing power monopsony, at the expense of choice and innovation. Alas, in healthcare, there are no panaceas, only tradeoffs, which are made politically.