Interesting. In every European country I know of, the private option is still available. Just vastly cheaper and more beneficial due to having to compete with a public option which covers basic necessities, surgery etc.
Yes, this is what I find a little odd about the US proposals. I've lived in UK and Spain and in both they have great free public healthcare for everyone, and if you (or your employer) want to layer private insurance on top you can. Wouldn't that be a much more appealing proposal to Americans?
Canadians can (and do) just cross the border and use private US health care. The vast majority of them live near the US border.