Your government funded health care budget alone would be enough to pay for a free-at-the-point-of-use system for the entire population like the UK.
Yes, all the inefficiencies would have to go, and that would mean people would have to get jobs that are more efficient and produce more bang for buck. That's life.
Maybe if the entire population was like the UK this might work - Americans are rather less healthy in general - and one of the "inefficiencies" the UK system does away with is paying for treatments that offer particularly bad value for money, so you'd have to tell a bunch of cancer patients that tough, they're not getting chemo, now go and die quietly, and even then it's not clear whether UK levels of cost efficiency are even possible in the US.
NICE is no different to insurance companies when it comes to hiding the value of a given drug. For cancer patients not given chemo, you're thinking of the US when your credit card bounces and you get dragged out of hospital.
I'm not aware of any cases when people are denied chaemotheropy on the NHS, yet I am aware of people in the Us struggling to pay $50k a year for something as basic as insulin.
Yes, all the inefficiencies would have to go, and that would mean people would have to get jobs that are more efficient and produce more bang for buck. That's life.