In my experience people in the US aren't envious of the NHS. Most of us are aware that the grass is not green on any side of that fence.
People in the US would like a system that works. That means not waiting 666 days for a CPAP. It also means not having the government strongly nudge you to off yourself with its assistance, as in Canada. And it means not having an ever-increasing number of deaths by waiting, as with the NHS, which typically don't happen here for most kinds of care.
Sadly, healthcare is expensive to provide regardless of who's paying. The NHS is able to provide even that troubled level of care because it pays its medical staff poorly by American standards, which it is able to do because it relies heavily on immigrants, which it is able to do in large part because those immigrants can't come to America and make 3x the salary since we make it incredibly difficult for foreign medical credentials to be recognized here. If we quit doing that tomorrow, the NHS would collapse by Friday.
If you think the problems of US healthcare are caused by too much „free market“ and could be solved or even marginally improved by an NHS-style socialized replacement with even more government interference, you have never seriously investigated the issue.
...except people in the US.