Health Care: A Third Way?

The central thesis of Michael Moore's "Sicko" appears to be that the problem with health insurance companies is that they have a fiduciary duty to maximize profit for their shareholders. His solution is, of course, to simply make the government the single payer for all health care costs, and points to European, Canadian, and most infamously, Cuban systems.

But isn't there a third market-based way to help ail our health care system that wouldn't call for as much redistribution of wealth? Couldn't the government create a corporation (a la Ginnie mae and Fannie mae) to exist as a national non-for-profit health care insurer? The Congress-chartered insurer could be funded by a one-time capitalization by the U.S. for $70 billion (about the market cap of United Health Group (UNH)). The non-for-profit could have a mandate to offer coverage to anyone that requested it (including plans for preexisting conditions), and it could offer below-market prices, especially for individuals who have pro-health lifestyles (no smoking or drugs, no obesity, etc).

The existence of a large-cap non-for-profit insurer on the market would put pricing pressure on independent insurers that would force them to lower prices and operate with lower overhead spending (which Moore said is higher in private companies than in government bureaucracies).

Any opinions on this from economists or medical professionals?