The NHS was a brilliant system when it started. The problem with it now is privatisation.
There's cost-cutting everywhere, and for the most part that means staff. When sisters ran wards, they didn't take crap from anyone. They kept the nurses in line, they dealt with lairy patients, they told the doctors what their department needed.
Now that it's run as a business (ie, for profit) it's a crap service. You can't run something like a health "service" at a profit without sacrificing something. And in this case, it's the quality of that service.
Losing nurses might save them millions per year, but that means less people around to deal with triage stuff like stitches and minor burns. Them reporting to a "department" which understands nothing about what the job entails and only cares whether what's "needed" affects their bottom line profits doesn't help anyone but the people sitting on their huge piles of money.
So the US could benefit from the old NHS, but not the privatised version. I'd go private in a heartbeat if I could afford it, because at least then you get seen and treated before you die.