Small(ish) OT, but after years and years of leaning in favor of a private healthcare system I have completely reversed my opinion.
I will spare you the ethical and moral reasons, and give you a practical one.
Private healthcare, being a business, cannot afford the investments of public one. Instead it operates following the Pareto principle where 20% of services and treatments cover 90%+ of patient needs.
Now this works with much joy over most of your life, but there are just too many edge cases over a life time where this will screw you.
E.g. A close friend of mine gave birth in a private clinic. The most luxurious one with almost a dozen people following her.
All of this: pointless. Her child had complications minutes after birth, and no single private hospital in our country has a pediatric intensive care unit, or, to label it more correctly a pediatric _reanimation_ unit.
The only private hospitals that do? University ones, as they operate on slightly different financial basis and incentives.
This goes beyond this example I have. It doesn't matter if you're in a country with good private healthcare (e.g. Switzerland) or a crap one, public healthcare is accepted to be a money loser for the greater good and will cover more services. Always.
Mind you, I'm not saying that a single public hospital will offer everything and private is bad, just stating that there's many situations where it's easier to find the service offered in public rather than private health care.