throwing my two cents in.
OP did not qualify what kind of privatized insurance she wanted.
It sounds like the European semi-private systems are all well regulated by the governments in those countries, in which case there is less chance for abuse of people who can't afford to pay.
i've lived in UK as a kid, Canada as a kid and adult and now US as an adult. When I was a kid in the UK, from what I remember everything was free including glasses and dental.
In Canada, I was only covered for things like prescriptions, glasses and dental with a private insurance plan ie through an employer, and it was usually only 75-80% covered, or max cap on certain items (think only $125 towards glasses when my high prescriptions cost $350+). My FIL was diagnosed with cancer and paid $0 for any treatment, including aftercare prescriptions, because he is over 65. (If it was me I would have had to pay some costs for drugs but nothing for hospital/surgery/chemo).
In the US, many things are about deregulation and small government - so it's very easy for the system to become bloated for the benefit of insurance companies which are for-profit businesses. That's why Obamacare was such a big deal for many people - even though it can be very expensive for some (and yes there are people whose same plans went up in price for premiums, which i blame entirely on the insurance companies' drive for profit), it meant that some people who would never even have been approved for insurance could now get some. Example - you now cannot be denied insurance for having a pre-existing condition. By that I mean, people who had no insurance who were then diagnosed with anything (cancer, chronic conditions, asthma etc) could be denied insurance and then have no option but to pay the ridiculous out of pocket expenses for healthcare. Or.... insurance companies could claim you had a pre-existing condition if you went to the dr for a stomach ache before you signed up and it then turned out to be stomach cancer after you got insurance. Even old people in the US on medicare (medicaid?) still need supplementary insurance as a) many hcps don't take medicare, and b) it doesn't cover as much stuff as in UK or Canada. My retired neighbour is paying more for supplementary than we are for company subsidized full insurance, when she is entitled to medicare.
I had DS in the US. Due to the work insurance we were on, we had to pay cash up front and get reimbursed later. Took me weeks before the birth to find out from the various providers an estimate of the costs so we knew how much to budget for. My original hospital bill was $7500 - just for the giving birth part and staying 2 nights - $6 for one extra strength ibuprofen pill. This was reduced to $4500 because I was paying cash... The OBGYN bill was $3000 or so. The epidural cost around $2000, and there were various other charges. That was for a fairly uncomplicated natural birth. If you couldn't afford insurance that would be $10-12k out of pocket at a minimum - any complications and the price skyrockets. I've spoken to friends who were on a US based insurance plan and even with coverage out of pocket expenses for a birth is around $10k. Many of my friends have chosen not to have a second child because they cannot afford the initial cost.
Also the cash up front prices are not necessarily better than excess/copay costs under insurance because it's all fixed. Paying cash at the pharmacy for prescription drugs on our old plan (with reimbursement later) meant that I was paying $100, when on US based insurance, i would pay $1 and the insurance would pay $19. But they do try telling you you're getting a discount paying cash ...
Three more points and then I promise I'll stop.
- www.washingtonpost.com/local/5-years-after-boy-dies-from-toothache-maryland-medicaid-dental-care-is-on-mend/2012/02/15/gIQANEJoGR_story.html?utm_term=.d91710e9b631
- In network vs Out of Network in the US is a huge deal. www.nytimes.com/2014/09/21/us/drive-by-doctoring-surprise-medical-bills.html?_r=0 and www.nytimes.com/2016/11/17/upshot/first-comes-the-emergency-then-comes-the-surprise-out-of-network-bill.html.
- Shrekli and the Epi-Pen price jacking. Even though that's drugs, the same kinds of things can happen in healthcare services.
These are the things that can happen if you go to a largely unregulated private healthcare system.