From a neutral standpoint, I think not outside of perhaps reasonable emergency care. You can't really ask a dead guy if he's got insurance and then treat him.

I do, however, think from a neutral standpoint providing standard preventative care is in the best interest of any country as it would make the percentage of able bodies and percentage of able bodied years the average citizen has higher, thus enabling more contribution to the economy.

I see it as differing from a right to a lawyer due to the lawyer thing mostly being a cover for the government there to provide a counter balance ensuring fairness verses the prosecutor's presence to press the case.

As far as right to compel people to do things, depends what you mean. I think from a neutral standpoint, there should only be the ability to compel others where it is necessary to protect the rights of others, especially those who cannot protect them themselves such as children. This would ensure your rights end where mine start, basically. I don't really see it as neutral to compel anyone to do anything they don't want to, outside of ensuring nothing one person does impinges on the ability of others to act in ways that don't hurt anyone else which is their right.

Not certain I can adequately explain the difference between individual right and society deciding to provide, exactly. To me, an individual right is something assured to make things even. So you have a right not to be mistreated because your nose is big, or your hair isn't coiffed in a style I enjoy, which to me makes as much sense as curtailing rights based on skin color or religion. A government has an interest in assuring rights to provide a stable underpinning for society to ensure productivity.

Something a society decides should be provided is an extra a society offers because it can afford to and the results will provide value to the society. This explains how certain countries are able to offer standardized care to all citizens if you follow it far enough. They also offer education inexpensively or freely to all provided they can display sufficient proficiency and ability. If you can take all training to become a doctor without incurring debt, then establish in practice also without incurring debt, there is no need to charge sky high fees because those who put in the effort can still have a higher standard of living on significantly less cashflow.

For the country, they get a deeper field of possibles to choose from when electing to offer expensive education and training, and can ensure trained coverage to all areas not just dense population centers. The expectation would be greater percentage viable workers and more from those viable workers due to trained providers having more healthy years during which to provide it.