The problem with US Healthcare is insurance companies. They're the reason that stories of a tylenol pill costing $10 at the hospital, because they control rates, only reimbursing at 10% sometimes, so billing specialists jack up the costs they submit to get reimbursed appropriately.
Interview any billing coder, they'll tell you how it works.
It's not free. We pay using taxes. Instead of paying a middle man whose sole purpose is to make money, you have a government run service that isn't profit driven. Is it efficient? No. Is there a better alternative? Also probably no but I haven't heard of one. If there is one that is being used somewhere in the world and isn't something theoretical, I would love to learn about it.
I will also say that these services aren't the best. What I mean is that the medical doctors are indeed competent and won't release you until you're cured or healthy enough depending on your condition, but expect to be at the hospital all day for an appointment that you got at least a month in advance.
Having said that, it sure beats going bankrupt or paying out of pocket. I don't mean to dunk on these state-driven services, but people need to be sober about these things.