Hospitals are required to take care of you, even if you have no insurance in the US. If you get a bill you cannot afford, you can negotiate a much lower rate with the hospital (I have done this and my family members have also done this).
I run my own business and so I need to pay for myself and my spouses healthcare. Obamacare actually made things worse for me. It doubled my costs (which was promised not to happen) and I was forced out of an otherwise great plan.
Getting sick is not even an issue. Medication is fairly inexpensive and if I have major surgery, I will only be out a couple thousand (the cost of a laptop).
I have many relatives in Canada and the only reason the system works there is because it borders the US. They get all of their regular care paid for by their taxes and the middle class drive over the border and get major surgery done.
The waiting lines are pretty long for most major surgeries and many older people die before they actually get it. The government there continues to promote getting checkups for specific diseases and disorders later and later in life because they don't have the facilities to get it done in a timely fashion for everyone.
NHS isn't the panacea everyone makes it out to be. There are no free lunches and when it comes down to it, a finite resource like healthcare has to have a filter/limiter. Since the majority of government run services are not that efficient and will not be able to keep up with demand or technology, it's much better to have a free-market/private care solution.
I agree with the sentiment of your post. We need to get rid of the bloated government-supported insurance companies and let the free market decide the price of everything..and offer a form of insurance to the poorest.