I think part of the problem with today’s health care system is the over-reliance on insurance companies. They are (rightfully) in the business of making money, and as a result they keep raising premiums.
What about the idea of competing with them by fostering the creation of non-profit insurance and/or medical co-ops? In a co-op, any profits would stay in the co-op to offset the additional cost of helping those currently lacking basic care.
You’ve pretty much described the “mutual aid societies” that once protected Americans against medical disasters — before government regulated them out of business for the benefit of the doctors and insurance companies.
David Beito’s wonderful book From Mutual Aid to the Welfare State describes them in detail.
The AMA condemned doctors that worked for a flat fee for these societies. Since the AMA controlled the licensing boards, physicians didn’t want to incur their wrath.
Even though the mutual aid societies served their members well during the Depression, insurance companies successfully lobbied for regulations requiring that mutual aid societies have large amounts of financial reserves on hand.
Thus, these effective co-op-like groups were essentially regulated out of business, putting us at the mercy of the often less efficient and less compassionate insurance companies.
The free market and human ingenuity creates amazing protection for us, but government intervention destroys it!