Insurance is a perfect example of things Government should run. Insurance is basicaly corporate socialism. Except instead of taxes, we pay premiums.
The benefits of a well run Government insurance provider would be tremendous. Unfortuneatly something like this only works when setup at the beginning (or very near). Now there is too much constituencies and leverage money to where it can’t be done correctly.
On the contrary, insurance is not socialism, it's more like gambling. Gambling that you're going to get sick/that your house will burn down/that you will be in a car crash. If you're wrong, you lose your ante/premium. But, if you're right, you win!
Having the government in the business means that market forces won't be at work, which means it will become a cash cow that pays out, at the expense of taxpayers, far more than it makes, and therefore milks taxpayers dry. (So what else is new.) The government has a program for flood insurance - of houses along ocean coasts, or which are even below sea level, that are subject to hurricanes, tsunamis, and other such. The government premium is far lower than free-market companies could possibly charge (and still make money), and indeed the program is vastly underwater, financially. The government doesn't give a hoot about profitability, and therefore, isn't a good steward of anything businesslike whatsoever. Why, they can just send armed agents to you and I to collect more money, if they need to. And they do and they will. Suggesting the government can fix a broken market is not to understand the market at all.