But can we still also get blackjack and hookers?

Unfortunately, you'll quickly find that the structure of the system will crush 'generous' insurance companies in short order.

it's all good as long as it's not publicly traded
- Or until profit-seeking private owners end up in charge
Angels who do good deeds lose to devils who don't.

That why the psychopaths are winning it for shareholders

New Zealand’s largest private health insurance provider (Southern Cross) is “run on not-for-profit principles”.

It’s not terrible, and seems to work. I guess the caveat is that their competition is a (mostly) functioning public healthcare system.

I’m not sure if it’s still the largest in the state, but Blue Cross Blue Shield of North Carolina is a non-profit, but they don’t seem to run in a very not-for-profit way. A long time ago, maybe 20 years ago, the board tried to switch it to a for-profit organization with the stated goal of going public and issuing stock options. The state didn’t allow them to do that, so the board started giving themselves lavish pay raises and arranging executive “retreats” in prime vacation destinations like Hawaii.

I don’t know how their denial rate compares to for-profit insurers, but they are a giant pain to deal with, and we have no other real options for the doctors we see and medications we take.
- I've worked for the non-profit insurance subsidiary of a charity hospital system, and part of the problem is that ANY of the competition is for profit. What that means is that the for-profit companies are effectively setting the baseline of coverage. Healthy people (or the HR department at the company) aren't as concerned with richness of benefit as they are with the lowest premium. Sick people, though? They've got a list of doctors and drugs they want to make sure are covered. So if the non-profit benefit is too rich it attracts all the sick people and suddenly the operating costs of the non-profit skyrocket and they go out of business. It's a weird model that can't be AS good as the mission wants to be.
  
  In my case the hospital system actually created a generic drug manufacturer themselves to undercut for-profit drug manufacturers. THAT was less daunting than trying to impact the insurance side any more than they already do.

Oh. Can it be run by the government, and provided to anyone who pays taxes (either currently, in the past, or someone that will in the future, like a child)?

That would be great.

I think you just invented socialized healthcare.

~~So kids don't get healtcare?~~
- Read it again carefully

Maybe start with clearly defined maximum pricing, publicly visible numbers, and strict punishment for denying doctor recommended claims. Also no "out of network". If your hospital accepts insurance, they are in network.

The venn diagram of massive profits and legit health care is just two circles that don't touch.

Kaiser Permanente is not for profit and not publicly traded. It’s not perfect, and it’s not cheap, but having dealt with America’s other insurance options, IMHO, it’s the best option in the US… if they’re in your state, and if you take the time to learn how to navigate an HMO.

Its not cheap, but it’s not nearly as expensive as the alternatives, and the don’t deny claims as much.

I had Kaiser for several years and it's the best version of the US healthcare system I've seen. It was reasonably cheap (compared to other insurance), they didn't jerk me around for referrals to their specialists, they have optometrists and pharmacies and stuff on site so you can get a few appts done in a day. It was convenient. Now, I'm sure some people have had a terrible time with them and I don't deny their experiences, but it worked for me.
- Same. I feel like, a few decades ago, you could make a good argument that PPO land gave you more choice in exchange for higher fees. But these days, the good private practices are completely slammed, and I honestly think it’s faster and easier to find a good doctor or specialist in Kaiser.
  
  The crazy thing is that my spouse works for one of America’s PPO insurance companies, and she’s rather use my Kaiser plans. The care is better and the out of pocket is way less.
Cory Doctorow also used them and wrote a post about it recently: https://pluralistic.net/2024/11/05/carcinoma-angels/
They take good care of their diabetic folks too

While it's good that you'd want to improve the system you'll have to look deeper as to why.

First results from my search:

Health insurance has about 3.3% net profit margin. United had 3.6% last data I found. (The rest of US industry average is 8.54%.)

The profit margins of insurance alone can't explain why your healthcare costs 40% more than any other country.

Considering insurance, and medical facilities negotiate to set their costs every year, I don't trust that their profit is so low.
I'd chalk this up to the kind of "creative accounting" they do in the movie industry. But that's just a guess, I don't have any knowledge on the matter.
A small percentage of hyper inflated prices over a large consumer base still equates to MASSIVE profits. It is a fundamental ethical flaw that we even allow for-profit medicine that is compounded by obvious cartel organization structures and corruption.
Some of that is "clever" accounting, the rest is that healthcare insurances don't have bargaining power with the providers. In Germany the state insurance companies have collective bargaining power so that for example an ambulance ride costs 500€ instead of 15000.
That’s by design.

The money is being paid out and the profits reaped elsewhere.