Medicare for All?

Robert Reich suggesting that Obamacare should really be Medicare for all. (Via Mark Thoma).  During my break, I had a conversation with a good friend's father, who happens to be a private doctor.  He's troubled by Obamacare and other sorts of government intervention in the medical field.  Reich suggests that much can be solved by making Medicare an insurance source for all Americans, like Social Security is a retirement fund for everyone.  He points to lower administrative costs, and how some of the problems private insurance companies are seeing are due to the "pre-existing health problems" mandate (my friend's dad also made note of this).  I tend to believe that something as crucial as insurance shouldn't be profit motivated, or nearly as profit motivated as it likely is.  I think a lot of problems with regards to health coverage is a poorly functioning insurance-health care partnership; there's a lot of limited coverage, you can only see certain doctors, doctors will only take certain insurance, etc.  On the other hand, I lived in Montreal for 3 years, so I experienced government health care, and it's a mess.  I wonder what (entirely) public insurance and (entirely) private doctors would look like.  Government supported health care can be messy, but poor people have to see doctors, too.