There is a study somewhere comparing the cost of health care to the consumer, Canada vs. the USA. It turns out that the Americans pay the same and in some cases more per capita than the Canadians who have socialised healthcare. Canadians pay taxes and Americans pay co-pays/per service etc..
The difference is that yes, Americans can choose (so can Canadians) but a good percentage have nothing. Whereas in Canada and the UK, at least everyone has something.
I've experienced all three systems and even though it has big problems, waiting lists and a doctor shortage, I think Canada has the best of the three in that it provides care for everyone with an American style of service. No system is perfect. Except Turkey apparently, my office mates (turkish) keep telling me...