Most "Western" countries have some sort of arrangement between the private and public systems.
In France, the system is effectively private with the state picking up 80% of the cost in most cases (am aware I may be out of date, French grans may correct). Some diseases have costs met in full, and many employers offer the 20% as an employee benefit. I think you get the full cost on retirement?
Anyway, you get the approximate picture.
Some of these 'mixes' are not efficient economically. many provide good care, but spend a lot on admin, and often don't use the workforce efficiently.
When funded properly, our NHS is very efficient, but of course, it now has to fight for funding. I have a feeling that to paraphrase Nye, there are not enough folk left to fight for it.
What is often forgotten as well, is how in some countries (US is the prime example) the insurance companies dictate care. They will, for example say that after 'X' operation, they will pay for Y nights' stay. There is not the flexibility to assess as there is in the NHS.
Having said that, now the NHS is 'outsourcing' care to private providers, this attitude is creeping in. My last joint replacement was outsourced to a private hospital (talk about 'poor doors'!) and it was explained that the NHS had paid for 2 nights' care. Any more, and I would be transferred to the local, overfull hospital. The private hospital could not be inefficient!
I have worked with nurses from all around the world. I have only ever heard one criticism of the NHS "you don't want to pay for it"!