They have a monopoly on these.
No WE have a monopoly on those. Because WE are the government.
And you're ignoring the fact that they are both less expensive and more effective than private health care coverage.
Our prison system is horrendous. I used to work in it.
Our prisons are working exactly as we want them to. If they are "horrendous", it's because that's what the American public want them to be. We Americans love punishment. The more severe, the better we like it. In fact we approve of "horrendous" punishment. Most of us approve of prisoners killing and gang-raping each other, regardless of their crimes.
It's sad, but it's true. We have become this ugly and uncaring toward each other. And we are this obsessed with the idea of 'righteous violence'.
Private education way outperforms public.
No, it doesn't. You only think it does because private schools get to select their students according to family income. Which as we all know has a huge effect on their performance.
When privately owned and operated schools have to serve all students, of all economic backgrounds, they fail miserably. Because they have to operate according to the prime directive of profit/loss over and above the prime directive of educating children regardless of their ability to pay. The few private companies that tried to provide open public education have failed. And now they no longer want to try.
Most often done with private contractors. (Medicaid/Medicare)
Actually, all the government outsourcing of health insurance has achieved was a massive increase in complexity and confusion, and a general increase in the cost of administration and medical services.
Are they failing now? (public utilities)
No, many of them are now severely price-gouging us, however. That's what private individuals do when they can buy government created and mandated monopolies. They use them to price-gouge everyone else for all they can get.