Our better model (in Canada, Quebec) is increasingly disliked by our population. The private sector is getting more popular, enough so that our government is thinking about banning it.
The overall point though is not to sit on the laurels and try to hammer in "one right way" of doing it, but to iterate until you find a legislative healthcare framework that works for your country and benefits most.
The lack of progress in US on health care front is an indictment of its political rigidity first and foremost.