Mutual of Omaha's Wild Kingdom, and a compendium of health care wonkery
Stan Brock, adventurer extraordinaire, graduated from Wild Kingdom, did some other stuff, and eventually went on to found Remote Area Medical, "... a non-profit, volunteer, airborne relief corps dedicated to serving mankind by providing free health care, dental care, eye care, veterinary services, and technical and educational assistance to people in remote areas..."
Getting back to the mutual part of it, a mutual insurance company is one where all the people who pay premiums are the owners of the company -- the money, all in one large pool, belongs to them, and when someone needs to pay for their heart transplant or chemotherapy or whatever, some administrative flunky in the insurance company writes a check to the doctor, hospital, lab, clinic, whoever. This is how health insurance used to be done in this country, and not all that long ago either.
When you get out in the world [or just cruise the blogosphere] and talk about how other countries do things and using their single-payer systems as a model for the US to emulate, you'll often hear: But France and Germany and Switzerland [and a host of others] all have private insurance companies! Which is true, but all those countries' private insurers are non-profit mutual companies, and they're so heavily regulated by their respective governments that they might as well be government-run.
And no, our present insurance companies are NOT going to go back to being non-profits, not ever. They could be forced to, but we haven't got a Congress that'll do that for us. Nor do I expect we'll get one anytime soon. The present DemoPlan [it's the Hacker plan] has zero provisions for converting the for-profits to non-profits, and is therefore nothing but continued corporate welfare for all the predators and parasites such as Aetna.
Yes, the entire system is sick right now. The profit motive has completely crucified it. When my mother entered nursing in 1973, there was no such thing as a private health insurance company -- all insurance companies were not-for-profit mutual companies, owned by their rate-payers. Private hospitals were generally not allowed by the states except when they did not practice any sort of critical care -- when my mother entered nursing, there was one (1) private hospital in the mid-sized city where we lived, and it specialized in cosmetic surgery. All other hospitals were non-profit municipal hospitals owned by people local to the community or by religious organizations such as the Catholic Church. Doctors made a good living, as did a lot of other people, but you did not have the Frist family of Tennessee getting obscenely wealthy by working the calculus, "if we cut hospital staffing by 20% we will lose $1 billion in judgements as people die due to lack of proper care but will save $2 billion in staffing costs" (no, I'm not joking about this, my mother got fired by HCA for ratting them out to state regulators for deliberately understaffing because they'd worked the numbers and figured out that the extra money paid out in judgements was less than the amount of money they saved in salaries and benefits).
Everybody made good money, and as a result, even though there was probably as many uninsured people as today, hospitals and doctors had the time and money to take on charity cases and it was rare that you had people dying because of lack of medical care. Of course, that was before all these expensive transplant surgeries and such became available, they'd transplanted a heart or two down in Houston but nobody ever imagined that transplantation would ever be anything other than an experimental treatment that didn't seem to work because of tissue rejection issues, but the point is that the system had the slack in it back then to provide better care to most people, whereas today it's pushed to the limits and those folks who got care in 1973 despite being uninsured get only the minimum care at the emergency room needed to keep them alive, then get thrown out on the streets again.
So yeah, it's maybe possible that the Hacker Plan would eventually evolve into a single-payer system, but don't hold your breath while you're waiting for that to happen, because they really do want you to just go away and die.