The NHS was founded by a guy who was glad his opponents were stupid politically and then the conservatives did a study and thought it was a pretty ok idea.
Just like in the US there is a nursing shortage.
Wait times in the UK are quite long for major surgeries and medical procedures. They are also quite good for seeing a GP, and there is reasonable flexibility in doing so. In the US, there is less flexibility and wait times for GPs are much longer. However, wait times for major procedures are not nearly as long.
Under the NHS 9,000 patients a year die to mistakes made in their care. According to various studies, in the USA, it was previously thought around 98,000 people died due to preventable medical mistakes. Now it's thought the number could be as high as 251,454. There are roughly 5x as many Americans ans Brits. These numbers may not quite compare, but they are defined similarly. It seems doubtful that the UK number is hugely worse.
The UK has 45% higher mortality rates after surgery than persons in the USA. Out of the top 7 most developed nations, the UK was the worst, the USA was the best. That being said, the average life expectancy for a Brit was 2 years longer.
Dental care in the UK is really bad in some areas. Some areas have really low rates of people attending the dentist. Yet some studies show that net outcomes are fairly equivalent, if not slightly favorable for the British. One third of Americans haven't been to the dentist in the last year, and it's largely those who can ill afford to visit the dentist. Although this is better than in Britain, it's hardly ideal.
There have been significant issues with the NHS's mental healthcare. 72% of residents found it to be either inadequate or very inadequate. I had a hard time finding anything comparable between the US and UK. Interestingly, one piece saw Obamacare as a model for improving mental healthcare., though that is just one man's opinion.
The average american spent $9451 on healthcare in 2015. The average Brit?: $4003. Life expectancy in USA? 78.74 years. UK? 81.50 years.
Conclusion: Spending double on healthcare has some advantages. Both systems prioritize different things, and have different advantages and disadvantages. But the NHS is hardly a system doomed to absolute failure.