Australia seems to have the best approach - everyone has access to basic services, but those who can afford to pay for Private Insurance get access to better hospitals, more comprehensive diagnostics and treatment, and much shorter waiting times.
Private Health care is a joke, it enables you to skip the queue if you're willing to pay for private health care but you won't find me using them.
I elected to cancel my private health care this year, it means in terms of tax I'm slightly worse off by a couple of hundred dollars (AUD) or so. But it means it goes to the Government rather than a private healthcare fund that seeks to make a profit.
If I do need elective surgery in the future though, it's likely far away as a healthy 34 year old. I'll pay for it in cash which likely would only be double my out of pocket expenses for an elective surgery anyway.