Yes, as I stated, if you have enough money, you can escape the NHS. I would argue that more people would get better care if they weren't being taxed so heavily to pay for the NHS, particularly if they aren't using it ("double payers"). The existence of a private system pinpoints a painful but obvious truth: that the NHS and systems like it are not the panacea of healthcare they're often hailed as being. For those who would otherwise have nothing available, systems like the NHS provide a safety net that ensures they get at least some level of care, eventually. For everyone else, it can mean long lines, denied care, and other challenges.
US health outcome numbers are skewed by a variety of factors such as gang violence, drug problems, a high rate of imprisonment, a higher percentage of rural communities where access to the latest and greatest healthcare tools isn't readily available, the fact that many low income individuals under 65 don't have regular access to medical care, overuse of defensive medicine, and a number of other things. It's the same sort of challenges you find when comparing any stats between very different countries. If you control for those differences, you'll find that some of the best care on Earth is available in the US, but it's an imperfect system.
Our system leaves some people without access to much care. The NHS leaves some people on a waiting list for years on end and drives others to head to other parts of Europe, India, Malaysia, and even the US for care. Each system has its issues; nobody has completely figured out healthcare just yet. The only way to realistically do so is to so cold and uncaring that even an economist might feel a twinge of moral concern. Nobody wants to pull the plug on grandma, and that's just step one to making a system that can provide a reasonable level of care to all. Step two is kids.