There has been a lot written about how for-profit and non-profit health care insurers already coexist and criticism from the left (about how private non-profits are insufficient) and the right (about how non-profits are going to destroy the for-profit industry). Both views are misguided in my opinion.
But first it is useful to remember that there is no prohibition against not for profit businesses in any industry, so if they somehow represent unfair competition, why do we not all shop at non-profit supermarkets, buy gas from non-profit gas stations and buy our TVs from non-profit electronics companies? The answer is, of course, that non-profit does not necessarily mean lower cost and capital flows to where it finds the highest return - so it is the very incentive for higher return that causes for-profits to be as efficient as possible.
So, there is really no reason to expect that promoting private non-profit health care providers will do any serious damage to the for-profit sector. For profits will continue to attract capital that will continue to promote more efficient management.
At the same time there is no real reason to expect that a government run, but self-funded, non-profit would be any better (or worse) than private entities. A self-funded government agency (of which examples abound - I used to work for one nobody has heard of, OPIC, and the reason no one has heard of it is that it runs on its own dime) has no more advantages than a private non-profit, except I suppose the government ensures it presence at the outset. Still, this could happen with the private sector as well fairly easily with well thought out legislation.
I think it is clear, or should be by now, the real problem with the health care system is the incentive for insurers to cherry pick the healthiest and wealthiest leaving the sick and the poor to rely on the public safety net. This costs us all immensely even though it is reasonably hidden-medicare and medicaid are ballooning as entitlement programs and this required the devotion of more and more revenue (tax dollars).
So I don't care if there is a public option or not, but I believe that regulating insurers behavior and mandating health insurance is essential. The whole point of insurance is pooling risk. This is what needs to happen so let's stop quibbling over non-profits.