(If my questions are indiscreet, don't give indiscreet answers ;))
On the first, that would be a big change you're suggesting. I don't know how well it would work. An example is Medicaid in the States, but there are numerous problems there, particularly with low-wage earners who are not "poor" enough to qualify but don't get a scheme with their jobs, and aren't rich enough to fund their own.
But essentially, you seem to me to think that a private system (bar a kind of Medicaid) would be more efficient than the public health service à la française. Where do you think that public service goes wrong?
French health care reform : undermining the Government security net
That was the result of a research work I did for my former employer, the idea being to explain to a US board how the French health care system worked and why it was being reformed and so on. I could set myself a target of making an update diary focused on answering your question. When through hell, just keep going. W. Churchill