This combo (system as you like to call it, although that leaves out a ton of stuff) also exists in the US as a non-profit. I said this already.
It doesn't help
What will help is doctors taking a paycut and mass layoffs.
The problems in the US are not on the payment side, they are on the service side: it's simply too expensive.
We need twice as many doctors, working half as many hours, for half as much pay.
That's what would fix the US.
I'm writing this from the UK where I use the NHS. I've also used the US system extensively and the Italian healthcare system extensively.
You need to get basic facts right if you want to be a part of the debate.