The reason is the strong lobby from the medical profession and pharmaceutical companies who fear a loss of profits and from, as that Bush idiot describes them, the 'haves and have mores'. In addition to that, the very citizens who would benefit from a better health care system have been brainwashed to fear it. It's amazing what you can achieve against the citizens of the US if you use the word 'Socialism'.
The experience of the UK shows that the medical profession and pharmaceutical companies actually gain when health care is available to all. So do the citizens, of course. To call the National Health Service 'socialist' is utter nonsense and intended to induce an irrational objection to it. All UK citizens who earn a wage, and their employers, pay a tax for the NHS costs and their own State pensions. The tax is, in essence, a proportion of each wage earner's income. Taxes are as much a feature of capitalist systems as socialist systems and so the UK tax is not 'socialist'. Taxes pay for all manner of common benefits in a community. In addition to the tax, most people pay a fixed fee for medication, irrespective of its real cost.
One great thing about a tax-based system rather than a private individual insurance scheme is that everyone benefits. Every child and adult, irrespective of age and health. Every ailment from 'flu to terminal cancer. No exceptions. Also, very importantly, it covers those who are out of work. It's an example of what a civilised society should do.
There are those who try take advantage of the system but they are few as a proportion of the total and successive governments during the past few decades have attempted to identify and close each loophole. Frankly, I'd rather put up with a few dodgers than have no NHS at all. I have never heard a UK citizen of any political persuasion suggest that the NHS and State pension scheme be scrapped.
UK citizens can still buy private health insurance if they wish. They still have to pay their tax contributions to the State scheme though. The advantages of private insurance are that you can have a private room and, handy for some people, you can choose the date of an operation. The doctors and consultants you see in a private hospital are the same people whom you see in the NHS hospital down the road! In fact, the private insurers are able to provide cheaper premiums because they don't have to provide a primary care service. They require you to see your GP and get a referral from him or her to a consultant on their books.