Thank you, just when I was starting to think I couldnt keep calling myself Libertarian, someone steps in and reminds me there are people that understand the balance properly. I typically call my opinions "Libertarian Socialist" but that sounds odd and the 'socialist' sounds superfluous when your talking about the principles of how to organize a society/country, you cannot discount a certain amount of collectivist thinking.
Bloated government = very bad ... but... Basic services = Good for all.
I favor allowing central government regulation of key things eg, FCC radio usage regulation (maybe not device compliance, but someone has to coordinate the radiofrequencies & FAA Air Traffic Control coordination. Sometimes a standard is good, but I've never met a corporate monopoly I would trust enough to be in control of something as important as either of the 2 examples above, so I'd rather be able to bloody vote out the people in charge of them.
I would say that if you were reforming things on such a huge scale as this would be, then from the start, the provision of health care should be universal.
As you said, there is nothing wrong with something that favors no group over another. I would rather not throw away things like herd immunity or deal with the weaseling of an insurance company while in pain or try deciding the best approach to my treatment based on how expensive it is, or risk charities not being able to afford to vaccinate enough of "the poor" to provide effective herd immunity and there be a pandemic that shuts down half a city due to staff home sick or dead. Healthcare should have an across the board universal base standard of cover and paid for by the state. No elaborate private hospitals subsidized by the sate nonsense either. There are decades of evidence & academic study on the economic benefit of universal healthcare to a sovereign nation. I wouldn't say you have to be required to use it or any such nonsense. Freedom to setup & use a private hospital as you please, a hospital bed with silk gown & plasma TV awaits. But I would be more than happy to pay the cost of universal healthcare in my taxes. Knowing clearly that it will be in my best interests both as a member of society and as a statistical member of a population pool who will be X% likely to suffer from incidents in the set {requires medical care} despite my best efforts to avoid needing it.