Why not?

Private health insurance companies are what most of us middle class people depend on to make sure we get health care. As long as you're in good health, and you keep your job, you're OK. The premiums are still big, but manageable. If you lose your job and you have health problems, then you might find your self in deep kimchi pretty quick. Especially if you have to try to make COBRA payments with no income.
Now, I understand the insurance industry. Ignorant people think that you pay your premiums and the money gets pooled together and services are paid for out of the premiums collected. NOT TRUE. Those premiums are invested and insurance companies are known as "institutional investors" like pension funds. Vast amounts of money are shoveled around in an attempt to grow the reserves of the company. It is out of these earnings that claims are paid. Stringent guidelines are set in order to control the claims and limit expenditures. Doctors find themselves answerable to the insurance companies and this will sometimes mean that they have to work without some of the tools they might need to help their patients who are unable or unwilling to pay for additional tests or proceedures.
Case in point, I went to a clinic because I had a very high fever. The doctor asked me about how long it had been going on and if I had trouble breathing sometimes. They gave me a chest X-ray which revealed a possible mass or scar tissue in my lung near my heart. I had to go to my doctor and get her to approve a CT scan. The insurance company told her that they wanted aother set of xrays instead. She told me that she was sending me for the scan, but warned me that the insurance company would probably refuse to pay a large part of it. I ended up paying somewhere around $400.00 or more and some additional money on top of it. I could tell she felt pressured into pushing the xray, but went ahead with the scan recommendation. I can imagine that she might get dropped from their list of PCP's or whatever if she did that sort of thing alot.
I'll have to go in for another one soon, I guess, because catching a hint of cancer now could give me a shot at beating it. It's very possible that it could take decades to develop, but by then, I wouldn't be their problem.
Meanwhile, executives of these companies reap huge bonuses and draw salaries that would make a burmese drug lord blush. They have golden parachutes and stock options. Health insurance is a major profit earning industry. We live in a time where questioning this arrangement puts you in the same category of Marx, Lenin, and carpet chewing liberals.
It does not have to be so.
There is another possibility. The major banks have to contend with credit unions. Credit unions used to be regarded as podunk bastard cousins by the major banks. They catered to poor and working class people. Now we see them making major inroads into the market share of the banking industry. Credit unions have a quaint, intoxicating business model. Account holders are not just customers, sheep waiting to be shorn, they are members of the credit union. They at least titularly have some power within the organization. The people that run them, do so for far less than bank managers and directors and they seem to do a better job of it.
Why not have health care unions or cooperatives and let them be run along the same lines as credit unions? You could call them anything you like, Health Mutuals, Health Co-ops etc. They would insure the members and there would be quarterly reports issued on claims paid and investment earnings and executive salaries. Perhaps a few doctors could be place on the board of directors. Perhaps local partnerships could be formed with clinics and hospitals. Patient complaints could be given more weight. Doctors could actually speak to other doctors regarding policies or even individual cases/claims. We wouldn't need vast government bureacracies besides the same small departments of insurance in each state which are already in place. (we'll have to be careful). Of course, these mom & pop insurance co-ops will have a hard time getting lobbyists and soft money to the right politicians, so maybe this will never happen, but I can dream can't I?