I'm sorry but that statement I bolded is entirely false. The US Constitution lays out the specific roles and limits of government. "Running shit" isn't their role. The federal government is to provide for the common defense, resolve state conflicts, manage interstate commerce, coin and print debt free money, and provide a court framework for citizens to exercise their rights laid out in the 'Declaration of Independence and Bill of Rights'.
That weak minded citizens and whorish politicians have allowed the Federal Government to become so large they can run all the things you listed doesn't mean it should. Government is force. Period. This might appeal to you when it uses its force to get you something you want (healthcare, food stamps, no bid military contracts) but it never relinquishes that force...never...and it will one day be turned on you. That's the history of "Civilization".
Ok, we'll have to disagree about whether seeing to the health of a population should be the responsibility of a government on the basis that it is a prerequisite for all the other stuff that a government is allowed to be responsible for.
Taking it another way, no way does it belong with insurance companies. If I'm sailing ships to East India and I want to take out insurance against the loss of my cargo and vessel, you and I might agree to an arrangement where I pay you X and if I lose a ship you pay me Y. Will a ship sink? I don't know. Neither do you. It might.
I might get robbed, or lose my shit in a house fire. If I feel the risk of these possibilities justifies the cost of buying insurance then I would chose to do so. Otherwise not.
Will I need medical aid at some point? Of course. Everyone will. It's an absolute certainty. What am I insuring against? The outside possibility that I don't stay healthy forever until the end of time?
Insuring against a universal inevitability is just plain weird. There's no cost versus risk analysis to be done since the likelihood of occurrence is 100%. Neither is there any question of winning the insurance bet, since it's safe to say at this point that insurance companies make money, leading us to conclude that they take in more than they pay out. If you're selling doughnuts that's great entrepreneurship but profiting from people's ill health and generating actuarially oriented 'health plans' is ghoulish as hell.
They should be put out on their ear. Costs would plummet and quality of care would rise. Instead they wrote 'em into law. Talk about your greasy smoke filled room deals.