Insurance has two primary purposes: communal assurance and bulk purchasing power.
Private systems differ from public systems in that the cost of providing their product is a "cost" itself, detrimental to the profit, thus the private insurer is motivated to deny service in the thousand ways we have heard of.
Public systems throughout the world have no inherent motive to deny service. Assuming that for the most part a society has a majority of healthy people (and if it didn't then the society would be in a crisis and unstable beyond the concerns of merely it's health insurance), then the revenue, service and goods payouts and administration costs is a zero sum game.
Abuse is irrelevant to this rumination because abuse is hostile to both systems equally. there is nothing inherent about for-profit systems that makes them more vigilant to abuse.
The effect of the cost, or tax, on public perception is irrelevant because in theory each system would be capable of using its purchasing powers equally and also equally be burdened by the ups and downs of the health needs of its members. Public systems are publicly audited by the nature of the times. If a population bulge has aged, or if a flu epidemic was raging who doubts the expense? Of course, private systems have motives beyond covering the costs, so to shareholders this easily becomes inexplicable in hard economic times.
The conclusion I am so poorly, but so necessarily getting to is that it would seem possible for an entity to exist privately that operated with the model of a public system. Theoretically, If a large group of people agreed to begin doing this, it could begin in a moment: people agreeing to assure each other that they will have access to the monies to pay the doctors and medical companies when they needed things from these doctors and medical companies. An insurance agreement.
I publish this clumsy diary because I need help understanding why this can't be done. I'm trying to walk through my head considering all the things I've sketched and I can't conceive why all the philanthropists or even just savvy activists haven't created a non-profit insurance company.
UPDATE* I realize money, money, money is the number one detriment so I would add that I'm thinking this in light of the fact that there are about to be 31 million new customers, looking for a good option.