I used to work as a cellist in the State Opera of Flanders (Belgium) in the 1980s. At one point I ended up flat on my back in the hospital for 3 weeks (compressed vertebrae due to an accident). I never saw a hospital bill. I had previously purchased a $20/month supplemental insurance plan which entitled me to a private room. Of course, part of my taxes went to the National health system. But when I couldn't work for the better part of 2 months, I did not have to worry about hospital bills, and I automatically received sick pay. The hospital had all my information already, as I was in the national database (similar to the VA system in the USA), and don't forget, this was the 1980s - early days for computer networks.
Just contrast that experience to one typically encountered in "The Best Medical System in the World". My wife, a solo family doc in CT, typically sees at most 3 or 4 patients per hour, often fewer, and her patients appreciate the time she takes with them. As her office manager, I can attest to the fact that we have to keep our overhead to an absolute minimum in order to stay in business. I'm sure that working in Canada or in the UK for the national health isn't always a dream job, but it must be nice not to have to fight for reimbursement!